Question

For an A.P., a= 25, d = -3. Find the value of n if S=112 ​

Answer 1

n = 7.

Explanation:

Sum S of an AP = (n/2)[2a + d(n - 1)]

112 = (n/2)[2*25 - 3(n -1)]

n/2 (53 - 3n) = 112

n(53 - 3n) = 224

-3n^2 + 53n - 224 = 0

3n^2 - 53n + 224 = 0

(3n - 32 )(n - 7 ) = 0

n = 7, 32/3

So n must be 7 as its a whole number.