Question

Find the sum of the first 20 terms of an A.P. whose n^th term is given by a_n = 5 + 2n. Can 52 be a term of this A.P.?

Answer 1

Given, a_n = 5 + 2n

For n = 1

a₁ = 5 + 2(1) = 7

For n = 2, a₂ = 5 + 2(2) = 9

For n = 3, a₃ = 5 + 2(3) = 11

∴ AP is 7, 9, 11, ....

Now, `S_n = n/2 [2a + (n - 1)d]`

`S_20 = 20/2 [2 xx 7 + (20 - 1) xx 2]`

= 10 [14 + 38]

= 10 × 52

= 520

Let T_m = 52

a + (m – 1)d = 52

7 + (m – 1)2 = 52

7 + 2m – 2 = 52

5 + 2m = 52

2m = 47

2m = `47/2`

m cannot be a rational number.

∴ 52 is not a term of this A.P.