A geometric sequence is defined recursively by an = 4an-1. The 10th term of the sequence is a10 = 3.5. What is a13?

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A geometric sequence is defined recursively by an = 4an-1. The 10th term of the sequence is a10 = 3.5. What is a13?

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Answer 1 · 2015-07-09T18:34:35

Using (I think) a different interpretation of the question than Spandy's answer (which I'm not certain I understand):
$XXXX$ $color(white)("XXXX")$ $a_{13} = 224$ $a_13 = 224$

Explanation:

Assuming the "givens" are:
$XXXX$ $color(white)("XXXX")$ $a_{n} = 4 a_{n - 1}$ $a_n=4a_(n-1)$
$XXXX$ $color(white)("XXXX")$ $a_{10} = 3.5$ $a_10 = 3.5$

$a_{11} = 4 \cdot a_{10} = 4 \cdot 3.5 = 14$ $a_11 = 4*a_10 = 4*3.5 = 14$

$a_{12} = 4 \cdot a_{11} = 4 \cdot 14 = 56$ $a_12 = 4*a_11 = 4*14 = 56$

$a_{13} = 4 \cdot a_{12} = 4 \cdot 56 = 224$ $a_13 = 4*a_12 = 4*56 = 224$

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A geometric sequence is defined recursively by an = 4an-1. The 10th term of the sequence is a10 = 3.5. What is a13?

1 Answer

Explanation:

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