Question

Part 1

The sixth term of a sequence is 128 and the common ratio is 2. Use the explicit formula for a geometric sequence to find
the first term.
Part 2
Use the information from Part 1 to write an explicit formula for the nth term of a geometric sequence. Find the 21st term
of the sequence.
Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include
all of Part 1 and Part 2 in your answer.

Answer 1

see explanation

Explanation:

Part 1

The n th term of a geometric sequence is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

Given
`a_(6)` = 128, then

a
`(2)^(5)` = 128, that is

32a = 128 ( divide both sides by 32 )

a = 4 ← first term

Part 2

`a_(21)` = 4
`(2)^(20)` = 4 × 1048576 = 4194304