Find the sum of each of the following arithmetic series:

34 + 32 + 30 + … + 10.

Here, First term = 34

Common difference = d = 34 - 32 = - 2

Last term = l = 10

Now, 10 = a + (n - 1)d

∴ 10 = 34 + (n - 1)(-2)

⇒ 10 - 34 = (n - 1)(-2)

⇒ - 24 = - 2n + 2

⇒ - 24 - 2 = - 2n

⇒ - 26 = - 2n

⇒ n = 13

⇒ n = 13

∴ there are 13 terms in this Arithmetic series.

Now, Sum of these 13 terms is given by

∴ S₁₃ = [2(34) + (13 - 1)(-2)]

= (13/2) × [68 + (12)(-2) ]

= (13/2) × [68 - 24]

= (13/2) × [44]

= 13 × 22

= 286

Thus, sum of 23 terms of this AP is 286.