Question

Find the sum of  the following arithmetic series:

34 + 32 + 30 +...+10

Answer 1

The given arithmetic series is 34 + 32 + 30 +.....+10.
Here, a = 34,d = 32-34 = -2 and l = 10.
Let the given series contain n terms. Then,

a_n = 10 

⇒ 34 + (n-1) × (-2) = 10                [a_n = a+ (n-1) d]

⇒ - 2n + 36 = 10 

⇒ -2n = 10-36=-26

⇒ n= 13 

∴ Required sum` 13/2 xx (34+10)                      [ s_n = n/2 ( a+l)]`

= `13/2 xx 44 `

= 286