Question

Find the sum given below:

–5 + (–8) + (–11) + ... + (–230)

Answer 1

–5 + (–8) + (–11) + ... + (–230)

For this A.P.,

a = −5

l = −230

d = a₂ − a₁ 

= (−8) − (−5)

= − 8 + 5

= −3

Let −230 be the n^th term of this A.P.

l = a + (n − 1)d

−230 = − 5 + (n − 1) (−3)

−225 = (n − 1) (−3)

(n − 1) = 75

n = 76

And S_n = `n/2(a+1)`

= `76/2[(-5)+(-230)]`

= 38 × (-235)

= -8930