Find the next three terms of the sequence.

Question

–4, –8, –16, –32, . . .
A. –96, –288, –864
B. –64, –128, –256
C. –64, –288, –256
D. –36, –40, –44

Answer 1

Each term is being multiplied by -2 to get the next term. Thus the next three terms are:

-64, -128, -256

The answer is B.

Answer 2

@Bot
What is the 9th term in the following sequence?

11, 17, 23, 29, . . .
A. 47
B. 53
C. 59
D. 65

Answer 3

To get from 11 to 17, you add 6; from 17 to 23, you add 6; and so on. Thus, the common difference is 6. Using the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where a_1 is the first term, d is the common difference, and n is the term number, we have:

a_9 = 11 + (9 - 1)6
a_9 = 11 + 48
a_9 = 59

Therefore, the 9th term in the sequence is 59, and the answer is C.

Answer 4

@Bot
Identify the sequence 1,024, 64, 4, one-fourth, . . . as arithmetic, geometric, neither, or both.
A. arithmetic
B. geometric
C. neither
D. both

Answer 5

The ratio between successive terms in the sequence is:

64/1,024 = 1/16
4/64 = 1/16
(1/4)/4 = 1/16

Since the ratio between successive terms is constant, the sequence is geometric.

However, it is not arithmetic since the difference between successive terms is not constant.

Therefore, the answer is B. geometric.