3.-18,108,-648 find the next three terms

Mathematics

1 answer:

Luba_88 [7]3 years ago

6 0

Answer:

Fifth term: 3888. Sixth term: -23320

Step-by-step explanation:

Notice that -18 is 6 times the first term (3): -6(3) = -18. Next, 108 is the product of -6 and -18. Thus, the common ratio is -6.

If a(1) is the first term and r is the common ratio, a formula for the nth term is

a(n) = a(1)*r^(n-1).

Here, a(n) = 3*(-6)^(n-1). As a check, let's determine whether this formula correctly predicts the 4th term (-648):

a(4) = 3*(-6)^(4-1) = 3* (-6)^3 = 3(-216) = -648. Yes.

Thus, the 5th term is a(5) = 3*(-6)^(5-1) = 3* (-6)^4 = 3(1296) = 3888,

and

the 6th term is a(6) = 3*(-6)^(6-1) = 3* (-6)^5 = -23320.

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