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elena55 [62]
4 years ago
13

Enter a recursive rule for the geometric sequence. 2,−6,18,−54,...

Mathematics
2 answers:
suter [353]4 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

A recursive rule allows us to obtain any term in the sequence from the previous term.

These are the terms of a geometric sequence with common ratio r

r = - 6 ÷ 2 = 18 ÷ - 6 = - 54 ÷ 18 = - 3

Thus to obtain a term in the sequence multiply the previous term by - 3

a_{n+1} = - 3 a_{n} with a₁ = 2

Luden [163]4 years ago
5 0

Answer:

a_n=-3a_{n-1} where a_1=2

Step-by-step explanation:

Recursive means you want to define a sequence in terms of other terms of your sequence.

The common ratio is what term divided by previous term equals.

The common ratio here is -6/2=18/-6=-54/18=-3.

Or in terms of the nth and previous term we could say:

\frac{a_n}{a_{n-1}}=r

where r is -3

\frac{a_n}{a_{n-1}}=-3

Multiply both sides by the a_(n-1).

a_n=-3a_{n-1} where a_1=2

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===================================

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