Let `{a_n}` be an arithmetic sequence with first term 77 and common difference -3. Find the maximum value of `sum_(k=1)^n \ a_k`

Let a_n , n ge 1 , be an arithmetic progression with first term 2 and common difference 4. Let M_n be the average of the first n terms. Then the sum_(n=1)^10 M_n is

The sum of first n terms of an arithmetic sequence is n^2+2n Find the common difference.

For each positive integer k, let S_k denote the increasing arithmetic sequence of integers whose firstterm is 1 and whose common difference is k. For example, S_3 is the sequence 1, 4, 7, 10.......Find thenumber of values of k for which S_k contain the term 361.

n, 3n, 5n,... is an arithmetic sequence. a) What is the common difference? b) Prove that the sum of first 'n' terms of this sequence is n^(3) . c) Then find the sum of 15 terms of the sequence 15,45,75,…..

Consider an arithmetic sequence with common difference 20. If the sum of reciprocals of two consecutive terms of this sequence is 1//24 find the first term of the arithmetic sequence .

Let a_n=16 ,4,1, be a geometric sequence. Define P_n as the product of the first n terms. Then the value of 1/4sum_(n=1)^oo P_n^(1/n) is _________.

Let a_n=16 ,4,1, be a geometric sequence. Define P_n as the product of the first n terms. Then the value of 1/4sum_(n=1)^oo P_n^(1/n) is _________.

If a_n is the n^(th) term of an A.P whose first term is a and common difference is d, prove that n=(a_n-a)/d+1

If sum_(k=1)^(n)k=45, find the value of sum_(k=1)^(n)k^(3).

Sum of the first 15 terms of an arithmetic sequençe is 495 and sum of first 25 terms is 1325 . i) What is the common difference of this sequence? ii) What is the first term? iii) What is the sum of first n terms of this sequence?