Question

Sum of first n terms of an ap is 2,4,6,.... Is 240 then the value of n

Answer 1

Given :-

the sum of first n terms of an AP 2, 4, 6,.... is = 240

here,

a = first term = 2

d = common difference

= a2 - a1 = 4 - 2 = 2

we know that,

Sn = n/2[2a + (n - 1)d]

➡ 240 = n/2[(2 × 2) + (n - 1)2]

➡ 240 × 2 = n(4 + 2n - 2)

➡ 480 = n(2 + 2n)

➡ 480 = 2n + 2n²

➡ 2n² + 2n - 480 = 0

taking 2 as common we get,

➡ 2(n² + n - 240) = 0

➡ n² + n - 240 = 0

splitting the middle term,

➡ n² + (16n - 15n) - 240 = 0

➡ n² + 16n - 15n - 240 = 0

➡ n(n + 16) - 15(n + 16) = 0

➡ (n + 16) (n - 15) = 0

➡ n = -16 or n = 15

since n can't be negative so n = 15