Question

Find the sum of  the following arithmetic series:

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

Answer 1

The given arithmetic series is `7 + 10 1/2 + 14 + ... + 84`.

Here, `a = 7, d = 10 1/2 - 7 = 21/ 2 - 7 = (21 - 4)/2 = 7/2` and `l = 84.`

Let the given series contain n terms. Then,

a_n = 84

⇒ `7 + (n - 1) xx 7/2 = 84`   ...[a_n = a + (n – 1)d]

⇒ `7/2 n + 7/2 = 84`

⇒ `7/2 n = 84 - 7/2 = 161/2`

⇒ `n = 161/7 = 23`

∴ Required sum = `23/2 xx (7 + 84)`   ...`[S_n = n/2 (a + l)]`

= `23/2 xx 91`

= `2093/2`

= `1046 1/2`