Question

The algebraic form for the sum of first n terms of an arithmetic sequence is 2n2 + 8n. How many consecutive terms of the sequence from the first, are to be added to get 330 ?

Answer 1

Sn = 2n2 + 8n (Given)

330 = 2n2 + 8n

2n2 + 8n – 330 = 0

n2 + 4n – 165 = 0

n2 + 15n – 11n – 165 = 0

n(n + 15) – 11 (n + 15) = 0

(n + 15) (n – 11) = 0

If n + 15 = 0 ⇒ n = – 15 (terms are not negative)

n – 11 = 0 ⇒ n = 11

∴ Hence, total 11 term from starting to be added.