Q7 of 97 Page 185

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

Let the first term be a and common difference be d.

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

k^th term = a_k = a + (k – 1)

∴ a + (k – 1)d = 5k + 1 ⇒ a + kd – d = 5k + 1

Comparing the coefficient of k, we obtain d = 5 and a – d = 1

⇒ a – 5 = 1

⇒ a = 6

Putting the value of a and d

∴

In an A.P., if p^th term is and q^th term is, prove that the sum of first pq terms is 1/2 (pq +1), where p q.

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If the sum of n terms of an A.P. is (pn + qn²), where p and q are constants, find the common difference.

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.

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