Find the sums given below:

7 + 10 + 14 +…. +84.

We have given a formulae to find sum of the series when first and last numbers are given.

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 = 84, a = 7

d = n₂ – n₁ = 10 - 7 = 3.5

a_n = a + (n-1)d

84 = 7 + (n-1)3.5

77 = 3.5(n-1)

22 = n-1

n = 23

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

= [ 2×7 + (2-1)3.5]

= [ 91]

⇒ .