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Oksi-84 [34.3K]
2 years ago
15

1; 4; 16; 64; ...what is the general term ​

Mathematics
1 answer:
Alborosie2 years ago
8 0

Given:

The sequence is

1, 4, 16, 64

To find:

The general term of the given sequence.

Solution:

We have, the sequence

1, 4, 16, 64

Here, the ratio between two consecutive terms is same. So, it is a geometric sequence.

First term is:

a=1

Common ratio is:

r=\dfrac{a_2}{a_1}

r=\dfrac{4}{1}

r=4

The nth term of a geometric sequence is

a_n=ar^{n-1}             ...(i)

Where, a is the first term and r is the common ratio.

Putting a=1 and r=4 in (i), we get

a_n=(1)(4)^{n-1}

a_n=4^{n-1}

Therefore, the general term of the given sequence is a_n=4^{n-1}.

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