Question

Find the sum of the series -5+(-8)+(-11)+...+(-230)

Answer 1

The general term of the series can be given as -3r-2 as the difference is -3 Now the summation of the series -3r-2 , where r is from 1 to 76 can be given as -3[ r(r+1)/2 ] - 2r Substituting value of r as 76, we get -3 [ (76 × 77 )÷ 2] -2×76 = {-3 [ 38×77] -158} = {-3[ 2926] -158} = { -8778-158 } = -8936

Answer 2

It is an AP with a = -5 and d = (-8 -(-5) )= -3
nth term = (a +(n-1)d)
⇒ -230 = -5 + (n-1)×(-3)
⇒ -230 = -5 - 3n + 3
⇒3n =228
⇒n = 76
now, sum = (n/2)(a + nth term)
                 =(76/2)(-5 + (-230))
                 = - 8930