Question

The sum of first n terms of an A.P. is 3n + n² then (i) find first term and sum of first two terms. (ii) find second , third and 15^th term.

Answer 1

We have:
S_n = 3n + n²
We know:
t_n = S_n – S_{(n – 1)}
Thus, we have:
t_n = 3n + n² – 3(n – 1) – (n – 1)²
= 3n + n² – 3n + 3 – n² – 1 + 2n
= 2n + 2

(i)
To find the first term, we will put n = 1 in t_n = 2n + 2.
Thus, we get:
t₁ = 2(1) + 2 = 2 + 2 = 4
To find the sum of the first two terms, we will put n = 2 in S_n = 3n + n².
Thus, we get:
S₂ = 3(2) + (2)² = 6 + 4 = 10

(ii)
To find the second term, we will put n = 2 in t_n = 2n + 2.
Thus, we get:
t₂ = 2(2) + 2 = 4 + 2 = 6

To find the third term, we will put n = 3 in t_n = 2n + 2.
Thus, we get:
t₃ = 2(3) + 2 = 6 + 2 = 8

To find the 15th term, we will put n = 15 in t_n = 2n + 2.
Thus, we get:
t₁₅ = 2(15) + 2 = 30 + 2 = 32