Geometric Sequence Formula a_n for 1/4, 1, 4, 16...

Published on March 30, 2026

Algebra

Determine the common ratio (r) and first term (a1) of the geometric sequence to find the explicit formula for the nth term, which is a_n = 4^(n-2).

Question

Answer

Here is the step-by-step solution to determine the formula for the

term of the given geometric sequence.

The given geometric sequence is:

The general formula for the

term of a geometric sequence is:

where

is the

term,

is the first term, and

is the common ratio.

Step 1: Identify the first term ().
The first term of the sequence is:

Step 2: Determine the common ratio ().
The common ratio

is found by dividing any term by its preceding term:

Check with the next pair:

Check again:

The common ratio is

Step 3: Determine the formula for the term ().
Substitute the values of

and

into the general formula

This formula can be simplified by noting that

Using the exponent rule

The problem asks for the values of

and

(as seen in the boxes provided in the image), and then implicitly for the formula for the

term.

Results for the boxes:

Final Formula for the term:

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