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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.

Respuesta :

Answer:

see explanation

Step-by-step explanation:

Part 1

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Given [tex]a_{6}[/tex] = 128, then

a[tex](2)^{5}[/tex] = 128, that is

32a = 128 ( divide both sides by 32 )

a = 4 ← first term

Part 2

[tex]a_{21}[/tex] = 4[tex](2)^{20}[/tex] = 4 × 1048576 = 4194304

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