Question

The first term of a geometric progression is 50 and the 4^th term is 1350. Determine the 5^th term.
1. 3050
2. 4050
3. 5050
4. 6050

Answer 1

Correct Answer - Option 2 : 4050

Given:

First-term of a GP = 50

The fourth term of a GP = 1350

Formula used:

The n^th term of a GP = ar^{n - 1}

Where, GP = geometric progression, r = common ratio, n = n^th term

Calculation:

a = 50, and let r be the common ratio, 4^th term = 1350

⇒ a₄ = ar^{n - 1}

⇒ 1350 = 50 × r^{(4 -1)}

⇒ r³ = 27

⇒ r = 3

a₅ = ar^{n - 1}

⇒ a₅ = 50 × 3^{(5 - 1)} = 50 × 3⁴

⇒ a₅ = 50 × 81 = 4050

∴ 5^th of a GP is 4050