2, a9=?...

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angelicafababaer21 @angelicafababaer21

September 2022 1 11 Report

Find the geometric term of each geometric sequence.
1. As=7, r=3, a10=?
2. a1=8, r=5, a7=?
3.a1=6, r=1/2, a9=?

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Verified answer

✏️SEQUENCES

==============================

$\large \bold{\blue{DIRECTIONS:}}$ Find the geometric term of each geometric sequence.

$\boxed{\sf a_n = a_1 \cdot r^{n-1}}$

#1: $\sf a_1=7, \: r=3, \: a_{10}= \: ?$

$\sf a_{10} = 7 \cdot 3^{10-1}$

$\sf a_{10} = 7 \cdot 3^{9}$

$\sf a_{10} = 7 \cdot 19,\!683$

$\sf a_{10} = 137,\!781$

$\large \therefore \underline{\boxed{\tt \purple{a_{10} = 137,\!781}}}$

$\:$

#2: $\sf a_1=8, r=5, a_7= \: ?$

$\sf a_{7} = 8 \cdot 5^{7-1}$

$\sf a_{7} = 8 \cdot 5^{6}$

$\sf a_{7} = 8 \cdot 15,\!625$

$\sf a_{7} = 125,\!000$

$\large \therefore \underline{\boxed{\tt \purple{a_{7} = 125,\!000}}}$

$\:$

#3: $\sf a_1=6, r=\frac{1}{2}, a_9= \: ?$

$\sf a_{9} = 6 \cdot \Bigg( \frac{1}{2} \Bigg)^{9-1} \\$

$\sf a_{9} = 6 \cdot \Bigg( \frac{1}{2} \Bigg)^{8} \\$

$\sf a_{9} = 6 \cdot \frac{1}{256} \\$

$\sf a_{9} = \frac{6}{256} \\$

$\sf a_{9} = \frac{3}{128} \\$

$\large \therefore \underline{\boxed{\tt \purple{a_{9} = \frac{3}{128}}}}$

==============================

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