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Lesson Posted 3 days ago

Vikas Mehra

I am an experienced ,qualified teacher with over 4 years of experience in teaching mathematics and economic....

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Lesson Posted 3 days ago

Vikas Mehra

I am an experienced ,qualified teacher with over 4 years of experience in teaching mathematics and economic....

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Lesson Posted 3 days ago Learn Class 10

Vikas Mehra

I am an experienced ,qualified teacher with over 4 years of experience in teaching mathematics and economic....

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Lesson Posted 3 days ago Learn Class 10

Vikas Mehra

I am an experienced ,qualified teacher with over 4 years of experience in teaching mathematics and economic....

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Lesson Posted on 23 Feb Learn Class 10 +1

Ashish K Sharma

I was a teacher and author and now, I am a Scientist. I have a PG degree in Mathematics as well a Diploma...

Arithmetic Progression Examples. Q: A man starts repaying a loan, with Rs 100 being its first instalment. If he increases the instalment by Rs 5/- every month, what amount he will pay in the 30th instalment? ... read more

Arithmetic Progression Examples.

Q: A man starts repaying a loan, with Rs 100 being its first instalment. If he increases the instalment by Rs 5/- every month, what amount he will pay in the 30th instalment?

Solution:

We know that the last  term of an AP is given by:

l = (a+ (n-1) * d).      ….. (1)

Now, as per the question,

a = 100,d = 5 and n = 30.

• l = (100 + (30-1) * 5) substituting the values in expression (1)
• l = 245

Thus, the amount to be paid in the 30th instalment will be Rs 245/-

***************************************************************

Q2. The Sum of the first four terms of an AP is 56, and, the sum of the last 4

terms is 112. If its first term is 11 then find out the number of terms of the

series.

SOLUTION.

We know that the Sum of the first n terms of an AP is given by:

Sn = (n / 2) * ((2 * a + (n-1) * d)). ……. (1)

Now, as per the question, substituting the relevant values in (1), we have,

• = (4 / 2) * ((2 * 11 + (4-1) * d)).
• 56 = 44 + 6d
• d = 2

Thus, now we have the first term as 11 and the common difference as 2.

Now, the last 4 terms of a AP is:  a + (n-1) * d, a + (n-2) * d , a + (n-3) * d and a + (n-4) * d.

Now, as per the question,

a + (n-1) * d + a + (n-2) * d + a + (n-3) * d + a + (n-4) * d = 112

• 4a+4nd – 10d = 112
• 2d(2n – 5) + 4 * 11 = 112 (substituting d = 2,a = 11)
• 4(2n-5) + 4 * 11 = 112
• 8n-20+44 = 112
• 8n = 112 – 24 = 88
• n = 11

Thus, the number of the terms of the series is 11.

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Lesson Posted on 05 Feb

Amey Nerkar

I am an experienced, qualified tutor with over 7 years of experience in teaching Science, Maths, English,...

Following steps are essential to learn English: 1. Read the chapter carefully. 2. Underline the hardwords. 3. Keep a dictionary with you. 4. Write the meaning of hardwords in the textbook itself. 5. Read the chapter again. read more

Following steps are essential to learn English:

2. Underline the hardwords.

3. Keep a dictionary with you.

4. Write the meaning of hardwords in the textbook itself.

1. 5. Read the chapter again.
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Lesson Posted on 05 Feb

Amey Nerkar

I am an experienced, qualified tutor with over 7 years of experience in teaching Science, Maths, English,...

Following steps are essential to improve your writing skills in English: 1. Read the title carefully. 2. Think about it calmly. 3. Jot down the bullet-points. 4. Decide the sequence of points. 5. Now, start elaborating above points. 6. Finally, conclude suitably. read more

Following steps are essential to improve your writing skills in English:

3. Jot down the bullet-points.

4. Decide the sequence of points.

5. Now, start elaborating above points.

6. Finally, conclude suitably.

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Lesson Posted on 05 Feb Learn Writing and grammar

Amey Nerkar

I am an experienced, qualified tutor with over 7 years of experience in teaching Science, Maths, English,...

Following steps are essential to learn grammar. 1. Have a suitable book of grammar. 2. Read the "Parts of Speech" first. 3. Try to understand the usage of "parts of speech" with the help of examples given in book. 4. Try to make similar sentences by yourself.
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Abhyansh Shukla

maths zone

1. Lack of double coincidence of want and exchange 2. Lack of divisibility 3 .problem of storing wealth 4 . Lack of standard of deferred payment
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