Question

Sum of the first n terms of an AP is 5n2 – 3n. Find the AP and also find its 16th term.

Answer 1

In an AP,

Sum of first n terms (Sn) = 5n² - 3n

So,

S1 = 5 × (1)² - 3 × 1 = 5 - 3 = 2

S2 = 5 × (2)² - 3 × 2 = 20 - 6 = 14

S1 = a1 (first term)

S2 = sum of a1 & a2

So,

Second term (a2) = S2 - S1 = 14 - 2 = 12

Common difference (d) = a2 - a1 = 12 - 2 = 10

So,

AP : a, (a + d), (a + 2d), ......

= 2, (2 + 10), (2 + 2 × 10), ....

= 2, 12, 22, ...

Now,

16th term = a + 15d = 2 + 15 × 10 = 2 + 150 = 152