Question

Find the sum of the following APs:

`1/15, 1/12, 1/10`, ... to 11 terms.

Answer 1

`1/15, 1/12, 1/10,` ... to 11 terms

For this A.P.,

a = `1/15`

n = 11

d = a₂ – a₁

= `1/12 - 1/15`

= `(5 - 4)/60`

= `1/60`

We know that

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

S₁₁ = `11/2[2(1/15) + (11 - 1)1/60]`

S₁₁ = `11/2[2/5 + 10/60]`

S₁₁ = `11.2[2/15 + 1/6]`

S₁₁ = `11/2[(4 + 5)/30]`

S₁₁ = `(11/2)(9/30)`

S₁₁ = `33/20`

Thus, the required sum of first 11 terms is `33/20`.