Question

Find an explicit rule for each geometric sequence using subscript notation. Use a calculator and round your answers to the nearest tenth if necessary.

The fifth term of a geometric sequence is 7. The sixth term is 3.5.

Answer 1

• aₙ = 224(1/2)ⁿ

Explanation:

Given GP with:

• a₅ = 7
• a₆ = 3.5

We can find the common ratio:

• r = 3.5/7 = 1/2

Using the nth term formula we can work out the first term:

• aₙ = a₁rⁿ⁻¹
• a₅ = a₁(1/2)⁴
• 7 = a₁ (1/16)
• a₁ = 7*16
• a₁ = 112

So the explicit rule is:

• aₙ = 112(1/2)ⁿ⁻¹ = 224(1/2)ⁿ