SOLUTION: This is one of the questions in a test that I wasn't able to answer. In the geometric sequence, a-sub1 = 1 and a-sub4 = 27, find a-sub7. A. 2992 B. 1953 C. 2187 D. 211

Algebra ->  Sequences-and-series -> SOLUTION: This is one of the questions in a test that I wasn't able to answer. In the geometric sequence, a-sub1 = 1 and a-sub4 = 27, find a-sub7. A. 2992 B. 1953 C. 2187 D. 211      Log On


   

Question 836400: This is one of the questions in a test that I wasn't able to answer.
In the geometric sequence, a-sub1 = 1 and a-sub4 = 27, find a-sub7.
A. 2992
B. 1953
C. 2187
D. 2110

Thanks,
Shayne
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: 27 = 3^3

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D=1 a%5B4%5D=27

In a geometric sequence,
r= common ratio
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29 for any natural number n

1%2Ar%5E%284-1%29=27
r%5E3=27 so highlight%28r=3%29
(You must know that 3%5E3=3%2A3%2A3=9%2A3=27 so you know where I got that r value).
a%5B7%5D=1%2A3%5E%287-1%29
a%5B7%5D=3%5E6

You see that choices A and D are not even multiples of 3, so they are not the answer.
(If they were multiples of 3, their digits would add up to 3, 6, 9, or some other multiple of 3).
3%5E6=3%5E%283%2A2%29=%283%5E3%29%5E2=27%5E2
I see immediately that B and C are also wrong, because the answer should be between 625 and 900:
25%3C27%3C30 <--> 625=25%5E2%3C27%5E2%3C30%5E2=900
It may be a typo (not necessarily your fault), or else someone is making a mistake in the calculations (and I say not me).
However,
2187=3%5E7 and 1953=3%5E2%2A7%2A31
I would choose answer highlight%28%22B+.+2187%22%29
and use judgement about confronting the teacher, or textbook maker about their mistake. If you already had the test, make sure you did not misread the question, and if the question was wrong, meekly point out that you knew the right answer, but were confused and frustrated by the choices given. Maybe you can gain more points that way.