Question

Find the sum of the following arithmetic series:

(-5)+(-8)+(-11)+...+(-230)

Answer 1

The given arithmetic series is  (-5)+(-8)+(-11)+...+(-230)

Here , a = -5 , d = -8 -(-5) = -8 + 5= -3 and l = 230

Let the given series contain n terms. Then,

a_n = -230 

 ⇒ -5 + (n-1) × (-3) = -230               [ a_n  = a + (n-1) d]

⇒ - 3n - 2 = -230 

⇒ -3n = -230 + 2 = -228 

⇒ n = 76 

`∴ "Required sum" = 76/2 xx [ ( -5) + (-230) ]            [ s_n = n/2 (a+l)]`

`= 76/2 xx (-235) `

= - 8930