Question

 what is the geometric sequence and the 8th term and the 10th term

Answer 1

The geometric sequence is decreasing by 0.5 * each term

common ratio = 0.5

an equation for this exact sequence would be

50(0.5)^x-1

Explanation:

To find the common ratio for a geometric sequence we can divide the previous term value by the next term value

so 50 / 25 = 0.5

and to check we can divide

25 / 12.5 = 0.5

So our common ratio is 0.5

Answer 2

Explanation:

Given sequence:

• 50, 25, 12.5, ...

The first term is 50 and the common ratio is:

• r = 12.5/25 = 25/50 = 1/2

The equation:

• tₙ = t₁rⁿ⁻¹
• tₙ = 50(1/2)ⁿ⁻¹

Find the 8th and 10th terms:

• t₈ = 50(1/2)⁷ = 0.390625
• t₁₀ = 50(1/2)⁹ = 0.09765625