Find the sum to n terms of the A.P, whose k^th term is 5k + 1

Solution:

It is given that k^th term of the A.P. is 5k + 1

i.e., a_k = (5k + 1)

It is known that general term of an A.P is a_n = a + (n - 1) d

a_k = a + (k - 1) d

5k + 1 = a + (k - 1) d

5k + 1 = kd + (a - d)

Comparing the coefficients of k , we obtain d = 5 and

⇒ a - d = 1

⇒ a - 5 = 1

⇒ a = 6

Therefore, S_n = n/2 [2a + (n - 1) d]

= n/2 [2(6) + (n - 1) (5)]

= n/2 [12 + 5n - 5]

S_n = n/2 [5n + 7]

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.2 Question 7

Find the sum to n terms of the A.P, whose k^th term is 5k + 1

Summary:

The sum to n terms of the above A.P whose kth term is 5k + 1 is n/2 [5n + 7]