Question

How do you find `S_n` for the arithmetic series given d=5, n=16, `a_n=72`?

Answer 1

`S_n=552`

Explanation:

`d=5 , n=16 ,a_n=a_16=72 , a_1= ? , S_n=S_16= ?`

We know `a_n= a_1+ (n-1)*d ; :. 72 = a_1+ (16-1) *5` or
`a_1= 72-75 = -3`

We know `S_n= n/2 {2a_1+ (n-1)*d} :. S_16= 16/2 {2*(-3)+ (16-1)*5}` or
`S_16= 8 *{-6+ 75} or S_16= 8 * 69 = 552`

`S_n=552` [Ans]