Question

Find the common ratio for the geometric sequence defined by the formula: an=40(2‾√)n−1 a n = 40 ( 2 ) n − 1

Answer 1

The ratio of the geometric sequence 40$2^{n-1}$ is 2.

Given that geometric sequence is 40*$2^{n-1}$ and we have to find the common ratio of all the terms.

Geometric sequence is a sequence in which all the terms have a common ratio.

Nth termof a GP is a$r^{n-1}$ in which a is first term and r is common ratio.

Geometric sequence=40*$2^{n-1}$

We have to first find the first term, second term and third term of a geometric progression.

First term=40*$2^{1-1}$

=40*$2^{0}$

=40*1

=40

Second term=40*$2^{2-1}$

=40*$2^{1}$

=40*2

=80

Third term=40*$2^{3-1}$

=40*$2^{2}$

=40*4

=160

Ratio of first two terms=80/40=2

Ratio of next two terms=160/80=2

Hence the common ratio of geometric sequence is 2.

Learn more about geometric progression at brainly.com/question/12006112

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