Find the sum of each of the following arithmetic series:

Question

Philoid · Accepted Answer

Here, First term = 7

Common difference = d = (21/2) - 7 = (7/2)

Last term = l = 84

Now, 84 = a + (n - 1)d

∴ 84 = 7 + (n - 1)(7/2)

⇒ 84 - 7 = (n - 1)(7/2)

⇒ 77 = (n - 1)(7/2)

⇒ 154 = 7n - 7 (multiplying both sides by 2)

⇒ 154 + 7 = 7n

⇒ 7n = 161

⇒ n = 23

∴ there are 23 terms in this Arithmetic series.

Now, Sum of these 23 terms is given by

∴ S₂₃ = [2(7) + (23 - 1)(7/2)]

= (23/2) × [14 + (22)(7/2) ]

= (23/2) × [14 + 77]

= (23/2) × [91]

= 2093/2

= 1046.5

Thus, sum of 23 terms of this AP is 1046.5.