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velikii [3]
3 years ago
14

Find an explicit rule for the nth term of the sequence.

Mathematics
1 answer:
nlexa [21]3 years ago
8 0

Answer:

An explicit rule for the nth term of the sequence will be:

a_n=-4\cdot \:2^{n-1}      

Thus, option (A) is true.

Step-by-step explanation:

Given the sequence

-4, -8, -16, -32, ...

A geometric sequence has a constant ratio r and is defined by

a_n=a_0\cdot r^{n-1}

Computing the ratios of all the adjacent terms

\frac{-8}{-4}=2,\:\quad \frac{-16}{-8}=2,\:\quad \frac{-32}{-16}=2

As the ratio 'r' is the same.

so

r=2

as

a_1=-4

Hence, the nth term of the sequence will be:

a_n=a_0\cdot r^{n-1}

substituting the values r=2 and a_1=-4

a_n=-4\cdot \:2^{n-1}      

Therefore, an explicit rule for the nth term of the sequence will be:

a_n=-4\cdot \:2^{n-1}      

Thus, option (A) is true.

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