Question

in an AP of 50terms ,the sum of first 11terms is 220and the sum of its last 20 terms is 2575 .find the AP​

Answer 1

Consider a and d as the first term and the common difference of an A.P. respectively.

n th term of an A.P., an = a + ( n – 1)d

Sum of n terms of an A.P., S n = n/ 2 [2a + (n – 1)d]

Given that the sum of the first 11 terms is 220.

11 / 2 [2a + 10d ] = 220

2a +10d= 40

a+5d=20--------------------------------(1)

the sum of its last 20 terms is 2575.

20 th term from the last = ( 50 – 20 + 1 ) th = 31 th term from the beginning.

a 31+a 32+....a 50 = 2575

20 a + 790 d = 2575

2a + 79 d = 257.5------------------------------(2)

solving (1) and (2),

we get d =

and a = 3.

Therefore, the terms in A.P. are