Find the 2nd term of a geometric progression whose common ratio is 1 / 5 and sum of first 4 terms is 124.8.

Find the 2nd term of a geometric progression whose common ratio is 1 / 5 and sum of first 4 terms is 124.8. Correct Answer 20

GIVEN:

Common ratio is 1/5 and sum of first 4 terms is 124.8 of a geometric progression.

CONCEPT:

Geometric progression formulas for calculating n^th term and sum of ‘n’ terms.

FORMULA USED:

n^th term of a geometric progression = ar^{(n - 1)}

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:

Using the formula we get,

a / = 124.8

⇒ a × / = 124.8

⇒ a × / = 124.8

⇒ 156a / 125 = 124.8

⇒ a = 100

∴ 2^nd term = 100 × (1 / 5)^{(2 - 1)}

⇒ 100 × 1 / 5