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Find the average of the first 12 terms of the arithmetic progression whose first term is 5 and 13th term is 53.

Find the average of the first 12 terms of the arithmetic progression whose first term is 5 and 13th term is 53. Correct Answer 27

Given:

First term is 5 and 13th term is 53

Formula used:

In an arithmetic progression, nth term = a + (n – 1) d, where a = first term and d = common difference

Sum of first n terms = n/2 ×

Average = sum of observations / number of observations

Calculation:

a = 5,

13th term = a + 12 d = 53

⇒ 5 + 12 d = 53

⇒ 12 d = 48

⇒ d = 4

∴ Sum of first 12 terms = 12/2 ×

⇒ 6 ×

⇒ 6 × 54

⇒ 324

Thus, average of first 12 terms = 324 / 12 = 27

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