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Find the average of first 20 terms of the arithmetic progression whose 7th term is 18 and the common difference is 3.

Find the average of first 20 terms of the arithmetic progression whose 7th term is 18 and the common difference is 3. Correct Answer 28.5

Given:

7th term is 18 and common difference is 3

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:

d = 3

7th term = a + 6d = 18

⇒ a + 6 × 3 = 18

⇒ a = 0

Sum of first 20 terms = 20/2 ×

= 10 ×

= 570

∴ Average of first 20 terms = 570/20 = 28.5

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