Find the sum of 23 terms of the A.P. 5, 9, 13, 17, ….

Concept use:

The formula for the sum (S) of the first n terms of an Arithmetic Progression (A.P.) is given by:

S = n/2 ×  [2a + (n - 1)d],

where a is the first term, d is the common difference, and n is the number of terms.

Calculations:

Given the sequence 5, 9, 13, 17, we can identify the following values: a = 5, d = 9 - 5 = 4.

We need to find the sum of the first 23 terms (n = 23), so we substitute these values into our formula:

S = 23/2 ×  [2 × 5 + (23 - 1) × 4] = 11.5 ×  [10 + 88] = 11.5 × 98 = 1127.

Therefore, the sum of the first 23 terms of the given arithmetic progression is 1127.