10. The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.

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Let's denote the first term of the arithmetic progression (AP) as a and the common difference as d
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Let's denote the first term of the arithmetic progression (AP) as a and the common difference as d read less
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Is there any relation between AM, GM, HM in Progressions?
Yes relationship is present and also equation is also present
Avinash
Divide 20 into 4 parts which are in A.P. and such that the product of first and fourth is to product of the second and third in ratio 2:3
Ans- 2,4,6,8 and 8,6,4,2 Let the four terms be a-3d,a-d,a+d,a+3d.. Then sum of all this will be 20 which will give 4a=20 or a=5 Following second part of the question (a-3d)(a+3d)/(a-d)(a+d) => ...
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Find the number of terms of the A.P: 7, 13, 19, ...., 205?
The first term, t1=a = 7. The common difference, b=13 - 7=6. Last term or the nth term, tn=a + (n-1)b = 205. So, we have, 7 + (n - 1)6 = 205 --> (n - 1) = (205 - 7)/6 = 33 --> n = 34. Answer: Number of terms is 34.
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How to find whether a sequence of numbers are in Arithmetic Progression or not?
Verify if the difference between the consecutive terms is the same.
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What is sum of an infinite geometric progression(GP)
S =a/1-r' where a is first term and r is common difference and less than 1
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