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irga5000 [103]
3 years ago
13

A geometric sequence is defined by the equation an = (3)3 − n.

Mathematics
1 answer:
Delvig [45]3 years ago
4 0
PART A

The geometric sequence is defined by the equation

a_{n}=3^{3-n}

To find the first three terms, we put n=1,2,3

When n=1,

a_{1}=3^{3-1}

a_{1}=3^{2}

a_{1}=9
When n=2,

a_{2}=3^{3-2}
a_{2}=3^{1}

a_{2}=3

When n=3

a_{3}=3^{3-3}

a_{3}=3^{0}
a_{1}=1
The first three terms are,

9,3,1

PART B

The common ratio can be found using any two consecutive terms.

The common ratio is given by,
r= \frac{a_{2}}{a_{1}}
r = \frac{3}{9}

r = \frac{1}{3}

PART C

To find
a_{11}

We substitute n=11 into the equation of the geometric sequence.

a_{11} = {3}^{3 - 11}

This implies that,

a_{11} = {3}^{ - 8}

a_{11} = \frac{1}{ {3}^{8} }

a_{11}=\frac{1}{6561}
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