Question

Find the sum given below:

`7 + 10 1/2 + 14 + ... + 84`

Answer 1

For this A.P.,

a = 7

l = 84

d = a₂ − a₁ 

= `10 1/2 - 7`

= `21/2 - 7`

= `7/2`

Let 84 be the nth term of this A.P.

l = a (n - 1)d

`84 = 7 + (n - 1) × 7/2`

`77 = (n - 1) × 7/2`

22 = n − 1

n = 23

We know that,

S_n = `n/2 (a + l)`

S₂₃ = `23/2 [7 + 84]`

= `23/2xx91`

= `2093/2`

= `1046 1/2`

Thus, the required sum is `1046 1/2`.