SOLUTION: Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively. (2 points) an = 9 • 4n an = 9 • (-4)n +

Algebra ->  Trigonometry-basics -> SOLUTION: Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively. (2 points) an = 9 • 4n an = 9 • (-4)n +      Log On


   

Question 1134911: Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively. (2 points)

an = 9 • 4n

an = 9 • (-4)n + 1

an = 9 • 4n - 1

an = 9 • (-4)n - 1
5
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use "^" to denote exponentiation; and use parentheses where required. The four answer choices should be

a(n) = 9*4^n
a(n) = 9*(-4)^(n+1)
a(n) = 9*4^(n-1)
a(n) = 9*(-4)^(n-1)

The 2nd and 5th terms are opposite signs, so the common ratio has to be negative; so the first and third answer choices can't be right.

The first term is -36.

The second answer choice gives a(2) = 9*(-4)^3 = 9*-64 = -576. not right.
The fourth answer choice gives a(2) = 9*(-4)^1 = 9*(-4) = -36. right.

The problem is more educational if you aren't given answer choices....

The 5th term 2304 is the 2nd term -36, multiplied by the common ratio 3 times:

2304%2F-36+=+-64+=+%28-4%29%5E3 --> the common ratio is -4

The 2nd term, -36, is the first term, multiplied by the common ratio once:

-36+=+a%281%29%2A%28-4%29
a%281%29+=+%28-36%29%2F%28-4%29+=+9 --> the first term is 9

The n-th term is the first term, multiplied by the common ration (n-1) times:

a%28n%29+=+%289%29%2A%28-4%29%5E%28n-1%29

... which is the 4th answer choice