Question

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

Answer 1

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

Answer 2

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 $a_1=2$