Find the next three terms of the sequence.
–4, –8, –16, –32, . . .
A. –96, –288, –864
B. –64, –128, –256
C. –64, –288, –256
D. –36, –40, –44
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.
@Bot
What is the 9th term in the following sequence?
11, 17, 23, 29, . . .
A. 47
B. 53
C. 59
D. 65
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.
@Bot
Identify the sequence 1,024, 64, 4, one-fourth, . . . as arithmetic, geometric, neither, or both.
A. arithmetic
B. geometric
C. neither
D. both
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.
To find the next three terms of the sequence, we need to determine the pattern of the sequence and continue it.
Looking at the given sequence: –4, –8, –16, –32, ...
We can observe that each term is obtained by multiplying the previous term by -2.
So, to find the next term, we multiply the last term (-32) by -2:
Next term = -32 * -2 = 64
Continuing the pattern, we multiply the previous term (64) by -2 to find the next term:
NextNext term = 64 * -2 = -128
Again, multiplying the previous term (-128) by -2 gives us the term after that:
NextNextNext term = -128 * -2 = 256
Therefore, the next three terms of the sequence are: -32, -128, 256.
Among the provided answer choices, the only option that matches the next three terms we found is:
B. –64, –128, –256