Find the average of first 5 terms of a geometric progression whose common ratio is 4 and first term is 5?

Find the average of first 5 terms of a geometric progression whose common ratio is 4 and first term is 5? Correct Answer 341

GIVEN:

The common ratio is 4 and the first term is 5 of a geometric progression.

CONCEPT:

Geometric progression formulas for calculating the sum of ‘n’ terms.

FORMULA USED:

Sum of ‘n’ terms of a geometric progression:

⇒ a(rⁿ - 1) / (r - 1) if r > 1

⇒ a(1 - rⁿ) / (1 - r) if r < 1

Where

a = first term, r = common ratio, n = number of terms

CALCULATION:

r > 1

Sum of first 5 terms = 5 × (4⁵ - 1) / (4 - 1)

⇒ 5 × (1024 - 1) / 3

⇒ 5 × 341

⇒ 1705

Average

⇒ 1705/5

⇒ 341