Question

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

The fourth term of the sequence is 234. The sixth term is 104.

The explicit rule for the geometric sequence is an

Answer 1

Hence the explicit rule is a(n) 1184.625 *(2/3)^n.

Answer 2

Explanation:

Geometric sequences are of the form a * b^x, where a and b are real constants.

We have a * b⁴ = 234 and a * b⁶ = 104.

Dividing the second equation by the first,

we get b² = 4/9, so b = 2/3.

When x = 4, a * b⁴ = 234.

=> a * (2/3)⁴ = 234, a = 1184.625

Hence the explicit rule

is a(n) = 1184.625 * (2/3)^n.