(i) − 5 + (− 8) + (− 11) + ………… + (− 230)

Solution:

Given to us that,

(−5) + (−8) + (−11) + ………… + (−230)

For the above given A.P.,

The first term, a = −5

The nth term, a_n= −230

Common difference, d = a₂−a₁ = (−8)−(−5)

⇒d = − 8+5 = −3

Let the n^th term of this A.P. be -230, and using the n^th term formula we arrive at,

a_n= a+(n−1)d

−230 = − 5+(n−1)(−3)

−225 = (n−1)(−3)

(n−1) = 75

n = 76

And, Sum of n term,

S_n = n/2 (a + l)

= 76/2 [(-5) + (-230)]

= 38(-235)

= -8930