The sum of first 7 terms of an A.P. is 49 and that of first 17 terms of it is 289. Find the sum of first n terms.
AP
75 Likes

Question

The sum of first 7 terms of an A.P. is 49 and that of first 17 terms of it is 289. Find the sum of first n terms.

KnowledgeBoat · Accepted Answer

Let the first term of A.P. be a and common difference = d. Given, sum of first 7 terms of an A.P. is 49, Given, sum of first 17 terms of an A.P. is 289, Subtracting (i) from (ii) we get, ⇒ a + 8d - (a + 3d) = 17 - 7 ⇒ a - a + 8d - 3d = 10 ⇒ 5d = 10 ⇒ d = 2. Substituting value of d in (i) we get, ⇒ a + 3(2) = 7 ⇒ a + 6 = 7 ⇒ a = 1. Hence, sum of n terms = n².

Mathematics

The sum of first 7 terms of an A.P. is 49 and that of first 17 terms of it is 289. Find the sum of first n terms.

AP

Related Questions

Find the sum of first 12 natural numbers each of which is a multiple of 7.

Find the sum of first 51 terms of an A.P. whose 2^nd and 3^rd terms are 14 and 18 respectively.

The first term of an A.P. is 5, the last term is 45 and the sum of its term is 1000. Find the number of terms and the common difference of the A.P.

Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.

Mathematics

The sum of first 7 terms of an A.P. is 49 and that of first 17 terms of it is 289. Find the sum of first n terms.

AP

Related Questions

Find the sum of first 12 natural numbers each of which is a multiple of 7.

Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.

The first term of an A.P. is 5, the last term is 45 and the sum of its term is 1000. Find the number of terms and the common difference of the A.P.

Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.

Find the sum of first 51 terms of an A.P. whose 2^nd and 3^rd terms are 14 and 18 respectively.