Here, first term = 5

Common difference = d = 13 - 5 = 8

Last term = l = 253

To find: number of terms in the Arithmetic series

So, n^th term is given by:

a_n = a + (n - 1)d

∴ 181 = 5 + (n - 1) × 8

⇒ 181 - 5 = 8n - 8

⇒ 176 = 8n - 8

⇒ 176 + 8 = 8n

⇒ 8n = 184

⇒ n = 23

Thus there are 23 terms in the arithmetic series.

Sum of first n terms of an AP is

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

∴ Sum of 23 terms is given by:

S₂₃ = [2(5) + (23 - 1)(8)]

= (23/2) × [10 + 176]

= (23/2) × 186

= 23 × 93

= 2139

Thus, sum of 23 terms of this Arithmetic series is 2139.