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Mathematics
Zoey Frost
27 October, 19:10
3.-18,108,-648 find the next three terms
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Izabelle Copeland
27 October, 19:26
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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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