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Oksi-84 [34.3K]
3 years ago
15

Enter a recursive rule for the geometric sequence. 6, −18, 54, −162, ...

Mathematics
1 answer:
svlad2 [7]3 years ago
5 0

Answer:

The required recursive formula is:

a_n=(-3)\times a_{n-1}

Step-by-step explanation:

We are given a geometric sequence as:

6,-18,54,-162,.....

Clearly after looking at different terms of the sequence we could observe that the sequence is an geometric progression (G.P.) with common ratio= -3 denoted by r.

Let a_n represents the nth term of the sequence.

This means that:

a_1=6, a_2=-18, a_3=54, a_4=-162,......

As the common ratio is -3.

so,

a_1=6\\\\a_2=-18=(-3)\times a_1\\\\a_3=54=(-3)\times a_2\\\\.\\.\\.\\.\\.\\.\\.\\.\\.a_n=(-3)\times a_{n-1}

Hence, the required recursive formula for the geometric sequence is:

a_n=(-3)\times a_{n-1}

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