Find the indicated nth term of the geometric sequence.
A)-327,680
B)-81,920
C)1,562,500
D)23
E)-312,500

Question

Find the indicated nth term of the geometric sequence. 
A)-327,680 
B)-81,920 
C)1,562,500 
D)23 
E)-312,500

Quizplus · Accepted Answer

We are not given the first term or the common ratio, so we cannot use the formula for the nth term of a geometric sequence. However, we can use the information given in the question stem to find the common ratio. The sequence is:

11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11
11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11*r
11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11*r^2
...
11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11*r^(n-1)

We can see that each term is obtained by multiplying the previous term by r. In other words, this is a geometric sequence with common ratio r. To find r, we can divide the second term by the first term, or the third term by the second term, and so on:

r = (11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11*r) / 11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11
r = 11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11 / (11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11*r)
r^2 = 11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11 / (11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11*r^2)
...

Simplifying each of these expressions, we get:

r = 16
r^2 = 256
r^3 = 4096

Now we can use the formula for the nth term of a geometric sequence:

a_n = a_1 * r^(n-1)

We don't know a_1, so we use the last term in the sequence:

a_11 = 11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11 * r^(11-1)
a_11 = 11eb80b1_af17_a08b_a291_892fdec7bbfd_TB8633_11 * 16^10

Simplifying, we get:

a_11 = -81920

Therefore, the answer is B.

Find the Indicated Nth Term of the Geometric Sequence