Find the sums given below:

(-5) + (-8) + (-11) +…… + (-230)

The sum of the series given by

S_n = [2a + (n-1) d]

Where n is the last term in the series

d is the common difference

a is the first term.

a_n = -230, a = -5

d = n₂ – n₁ = (-8) – (-5) = -3

n^th term a_n = a + (n-1)d

-230 = (-5) + (n-1)(-3)

-225 = -3(n-1)

75 = n-1

n = 76

The sum of the series is S_n = [2a + (n-1) d]

= [ 2×(-5) + (76-1)(-3)]

= 38 [ -235 ]

⇒ 8930