Question

Find the sum of the A.P. 7, `10 1/2`, 14, ... 84.

Answer 1

A.P.  = 7, `10 1/2`, 14, ... 84

a₁ = 7, a₂ = `10 1/2`, l = 84

Common difference, d = a₂ – a₁

= `10 1/2 - 7`

= `21/2 - 7`

= `(21 - 14)/2`

= `7/2`

We know that,

l = a_n = a + (n – 1) × d

⇒ `84 = 7 + (n - 1) xx 7/2 `

⇒ `84 - 7 = (n - 1) xx 7/2`

⇒ `77 = (n - 1) = 7/2`

⇒ `77 xx 2/7 = (n - 1)`

⇒ n – 1 = 11 × 2

⇒ n = 22 + 1

⇒ n = 23

We know that,

`S_n = n/2 [a + l]`

= `23/2 [7 + 84]`

= `23/2 [91]`

= `2093/2`

= `1046 1/2`