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Virat replied | 4 days ago

n=34

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Saurabh replied | 3 days ago

n= 34.

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User 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Find the A.P whose 10th term is 5 and 18th term is 77?

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Tapas replied | 6 days ago

Let the first term be a and the common difference be b.
So, the 10th term: t10 = a + 9b = 5.
and, the 18th term: t18 = a + 17b = 77.
So, from t17 - t10 we get: 8b = 77 - 5 = 72.
This gives: b = 9.
From t10 we get: a = 5 - 9b = 5 - 9x9 = -76.
So, a = -76, b = 9 and the A.P is:-
-76, -67, -58, -49, ..... (Answer).

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S

Suresh 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

In a certain A.P the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term?

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Tapas replied | 6 days ago

Let the first term be a and the common difference be b.
So, by the given condition:-
t24 = 2 x t10 --> a + 23 b = 2 ( a + 9b) = 2a + 18b.
This gives: a = 5b.
So, the 72nd term: t72 = a +71b = 5b + 71b = 76b.
and the 34th term: t34 = a + 33b = 5b + 33b = 38b = 76b/2 = t72/2.
So, the 72nd term is twice the 34th term. (Proved)

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Granth 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

The sum of the first six terms of an A.p is zero and the fourth term is 2. Find the sum of its first 30 terms?

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Tapas replied | 5 days ago

Let the first term be (a - 5b) and the common difference be 2b.
So the six terms are: (a - 5b), (a - 3b), (a - b), (a + b), (a + 3b), (a + 5b).
By the given conditions:-
Sum of six terms = (a - 5b) + (a - 3b) + (a - b) + (a + b) + (a + 3b) + (a + 5b) = 6a = 0.
So, a = 0.
The fourth term = a + b = 2 --> 0 + b = 2 --> b = 2.
So, for the A.P. the first term...  more»
Let the first term be (a - 5b) and the common difference be 2b.
So the six terms are: (a - 5b), (a - 3b), (a - b), (a + b), (a + 3b), (a + 5b).
By the given conditions:-
Sum of six terms = (a - 5b) + (a - 3b) + (a - b) + (a + b) + (a + 3b) + (a + 5b) = 6a = 0.
So, a = 0.
The fourth term = a + b = 2 --> 0 + b = 2 --> b = 2.
So, for the A.P. the first term x = (a - 5b) = -10. The common difference, y = 2b = 4.
Sum of 1st 30 terms, S30 = (n/2)[2x + (n-1)y] = 15 x [ -20 + 29 x 4] = 1440. (Answer) «less

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S

Supriyo 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

An A.P consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term?

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Tapas replied | 6 days ago

Let the first term be a and the common difference be b. So,
t1 = a = 7 and t60 = a + 59b = 125.
From above, we get:-
t60 - t1 = 59b = 125 - 7 = 118.
So, b = 118/59 = 2.
Hence, the 32nd term, t32 = a + 31b = =7 + 31x2 = 69. (Answer)

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N

Nitesh 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers?

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Tapas replied | 6 days ago

Let the 3 terms are (a - b), a, and (a + b).
So,
(a - b) + a + ( a + b) = 27
=> 3a = 27
=> a = 9.
Now the product is 648. So,
(9 - b) x 9 x (9 + b) = 648
=> (81 - b^2) = 648/9 = 72
=> b^2 = 81 - 72 = 9
=> b = =3 or b = -3.
For, b = 3, the numbers are:
(9 - 3), 9, (9 + 3) = 6, 9, 12
or
(9 - (-3)), 9 , (9 + (-3)) = 12, 9, 6
The...  more»
Let the 3 terms are (a - b), a, and (a + b).
So,
(a - b) + a + ( a + b) = 27
=> 3a = 27
=> a = 9.
Now the product is 648. So,
(9 - b) x 9 x (9 + b) = 648
=> (81 - b^2) = 648/9 = 72
=> b^2 = 81 - 72 = 9
=> b = =3 or b = -3.
For, b = 3, the numbers are:
(9 - 3), 9, (9 + 3) = 6, 9, 12
or
(9 - (-3)), 9 , (9 + (-3)) = 12, 9, 6
The three numbers are 6, 9, 12 or 12, 9, 6 (Answer) «less

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A

Anmol 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Write the first four terms of the A.p, when the first term a and the common difference d are given: a = 10, d = 10?

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Tapas replied | 5 days ago

The first four terms are 10, 10 + 10, 10 + 2x10, and 10 + 3x10.
So, the terms are: 10, 20, 30, 40.

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S

Samskriti 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

For the given A.P write the first term and the common difference: 3, 1, -1, -3, …..?

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Tapas replied | 5 days ago

The first term is 3.
The common difference = 1-3 = -2.

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S

Shreyansh 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

If the 3rd and the 9th terms of an A.P are 4 and -8 respectively, which term of this A.P is zero?

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Tapas replied | 6 days ago

Let the first term and the common difference are a and b.
So, the third term: t3 = a + 2b = 4.
and, the 9th term: t9 = a + 8b = -8.

So, t9 - t6 = 6b = -8 - 4 = -12 --> b = - 2.

So, from the expression of t3, we get:
a = 4 - 2b = 4 + 4 = 8.

Let us consider that the nth term is zero. So:

tn = a + (n-1)b = 0 --> 8 + (n-1)(-2)...  more»
Let the first term and the common difference are a and b.
So, the third term: t3 = a + 2b = 4.
and, the 9th term: t9 = a + 8b = -8.

So, t9 - t6 = 6b = -8 - 4 = -12 --> b = - 2.

So, from the expression of t3, we get:
a = 4 - 2b = 4 + 4 = 8.

Let us consider that the nth term is zero. So:

tn = a + (n-1)b = 0 --> 8 + (n-1)(-2) = 0 --> 8 -2n +2 = 0 --> 2n = 10 --> n = 5.

Answer: The 5th term of the series is zero. «less

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P

Preeti 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

If 9th term of an A.P is zero, prove that its 29th term is double the 19th term?

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Ram Mohan replied | 22 Nov

Let 'a' be the first term and 'd' be the common difference of the given A P. If Tn stands for nth term of this A P, then we get T9 = a + 8d= 0 ( Given).
T19 = a + 18 d = ( a + 8 d) + 10 d = T9 + 10 d = 0 +10 d = 10d
T29 = a + 28 d = (a + 8 d) +20 d = T9 + 20 d = 0 + 20 d = 20d =2 *10 d= 2 * T19.

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Prakash 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Determine the A.p whose third term is 16 and the difference of 5th from 7th term is 12?

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Chandan replied | 22 Nov

an= a+(n-1)d
an=10+(30-1)*(-3)
=10-87=-77
30th term is -77

a + (3 ? 1) d = 16
a + 2d = 16 ... (i)
a7 ? a5 = 12
[a+ (7 ? 1) d] ? [a + (5 ? 1) d]= 12
(a + 6d) ? (a + 4d) = 12
2d = 12
d = 6
From equation (i), we get,
a + 2 (6) = 16
a + 12 = 16
a = 4
Therefore, A.P. will be
4, 10, 16, 22, …

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R

Ramya 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

What is the 30th term of a given A.P: 10, 7, 4,....?

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Chandan replied | 22 Nov

a3 = 16

a + (3 ? 1) d = 16
a + 2d = 16 ... (i)
a7 ? a5 = 12
[a+ (7 ? 1) d] ? [a + (5 ? 1) d]= 12
(a + 6d) ? (a + 4d) = 12
2d = 12
d = 6
From equation (i), we get,
a + 2 (6) = 16
a + 12 = 16
a = 4
Therefore, A.P. will be
4, 10, 16, 22, …

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S

Sarvepalli 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Which term of the A.P: 3, 8, 13, 18, ……, is 78?

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Chandan replied | 22 Nov

tn = a + (n - 1) d
78 = 3 + (n - 1)5
78 = 3 + 5n - 5
78 = - 2 + 5n
78 + 2 = 5n
80 = 5n
80/5 = n
16 = n
n= 16

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K

Krity 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

The 17th term of an A.P exceeds its 10th term by 7. Find the common difference?

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Sarvajeet Kumar replied | 23 Nov

1.

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T

Thomas 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Find the sum of the following A.P: 1, 3, 5, 7,......, 199?

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D

Deepak 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

A, b and c are in A.P. Prove that b + c, c + a and a + b are in A.P?

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A

Aishwarya 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Find the sum of the series 51 + 50 + 49 +..... + 21?

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A

Abinaya 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

How many terms of A.P -10, -7, -4, -1,...... must be added to get the sum -104?

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M

Mukundan 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

If the sum of p terms of an A.P is 3(square of p) + 4p, find its nth term?

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H

Harish 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

If the given sequential is an A.P then find the common difference d and write three more terms: 2, 4, 8, 16,…… ?

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A

Amanbir 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Find the missing term of an A.P: 2, __, 26?

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S

Sona 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

An A.P consist of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term?

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Nagesh 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Which term of the A.P: 3, 15, 27, 39,.......... will be 132 more than its 54th term?

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A

Show previous answers

Meenakshi replied | 03 Nov

If d (common difference) is same for different values of n , then

the given list of numbers form an AP .

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S

Sourabh replied | 04 Nov

As all the answers say
If the difference is constant its in AP.
I will like to add one point that nothing but just practice can help you get through this problem.

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A

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Anurup replied | 02 May

a=1st term ; r=common ratio
Sum=a/(r-1), if r>1
Sum=a/(1-r), if r<1

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Ashutosh replied | 13 May

it is a/(1-r) provided |r|<1 otherwise series can't converge.

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