Question

Find the sum of the A.P., 14, 21, 28, ......, 168.

Answer 1

Here a = 14 , d = 7 and t_n = 168

t_n = a + (n – 1)d

`=>` 168 = 14 + (n – 1)7

`=>` 154 = 7n – 7

`=>` 154 = 7n – 7

`=>` 161 = 7n

`=>` n = 23

We know that,

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

`=> S_23 = 23/2 [2 xx 14 + (23 - 1)7]`

= `23/2 (28 + 154)`

= `23/2 xx 182`

= 2093

Therefore, the sum of the A.P., 14, 21, 28, ......, 168 is 2093.