What is the 10th term of the geometric sequence 400, 200, 100?

Solution:

The given geometric series has :

First term = a = -3

The common ratio r = 200/400 = 100/200 = 1/2

The sum of a infinite geometric series is given by:

Tn = a rⁿ⁻¹

T₁₀ = 400 × (1/2)¹⁰⁻¹

T₁₀ = 16 × 25 × (1/2)⁹

T₁₀ = 2⁴ × 2⁻⁹ × 25

T₁₀ = 2⁻⁵ × 25 = 25/32

What is the 10th term of the geometric sequence 400, 200, 100?

Summary:

The 10th term of the geometric sequence 400, 200, 100 is 25/32.