Question

In an A.P. if S_n  = 4n² − n, then

1. find the first term and common difference.
2. write the A.P.
3. which term of the A.P. is 107?

Answer 1

(i)

S  = 4n² − n

We know

a₁ = S₁  ⇒ 4(1)² − (1) = 3

⇒ a₂ = S₂ − S₁

₌ 4(2)² − (2) − {4(1)² − 1}

= 4 × 4 − 2 − {4 − 1}

= 14 − 3

a₂  = 11

d = a₂ − a₁

d = 11 − 3

d = 8

(ii)

a₁, a + d, a + 2d

3, 3 + 8, 3 + 2 × 8

AP = 3, 11, 19 .....

(iii)

a = 3, d = 8, a_n = 107

a_n = a + (n − 1)d

⇒ 107 = 3 + (n − 1)8

⇒ `104/8 = n − 1`

⇒ 13 + 1 = n

⇒ n = 14