What are the next three terms in the sequence?
–6, 5, 16, 27, …
A. 38, 49, 60
B. 37, 47, 57
C. 36, 45, 54
D. 36, 46, 57
The common difference between terms is 11 (5 - (-6) = 11, 16 - 5 = 11, 27 - 16 = 11), so we can continue the pattern by adding 11 to the last term:
–6, 5, 16, 27, 38, 49, 60
The answer is A. 38, 49, 60.
Geoff planted dahlias in his garden. Dahlias have bulbs that divide and reproduce underground. In the first year, Geoff’s garden produced 8 bulbs. In the second year, it produced 16 bulbs, and in the third year it produced 32 bulbs. If this pattern continues, how many bulbs should Geoff expect in the sixth year?
A. 64 bulbs
B. 512 bulbs
C. 128 bulbs
D. 256 bulbs
We can see that the number of bulbs is doubling each year. Therefore, in the fourth year, there should be 64 bulbs (32 x 2), in the fifth year there should be 128 bulbs (64 x 2), and in the sixth year there should be 256 bulbs (128 x 2).
The answer is D. 256 bulbs.
What are the first four terms of the sequence represented by the expression n(n – 2) – 3?
A. –5, –2, 1, 4
B. –4, –3, 0, 5
C. –3, 0, 3, 6
D. –2, 0, 2, 4
If we substitute n = 1 into the expression n(n – 2) – 3, we get:
1(1 – 2) – 3 = -2 – 3 = -5
If we substitute n = 2 into the expression n(n – 2) – 3, we get:
2(2 – 2) – 3 = 0 – 3 = -3
If we substitute n = 3 into the expression n(n – 2) – 3, we get:
3(3 – 2) – 3 = 3 – 3 = 0
If we substitute n = 4 into the expression n(n – 2) – 3, we get:
4(4 – 2) – 3 = 8 – 3 = 5
Therefore, the first four terms of the sequence are -5, -3, 0, and 5.
The answer is B. -5, -3, 0, 5.
A car traveling at 23 mi/h accelerates to 46 mi/h in 5 seconds. It maintains that speed for 5 seconds and then slows to a stop in 5 seconds. Which graph shows the car’s speed over time?
To find the next terms in the sequence, we need to identify the pattern or rule that governs how each term is obtained from the previous one.
By looking at the sequence, we can observe that each term is obtained by adding 11 to the previous term. The difference between each term is a constant value of 11.
Using this pattern, we can find the next three terms by adding 11 to the last term given in the sequence:
27 + 11 = 38
38 + 11 = 49
49 + 11 = 60
Therefore, the next three terms in the sequence are 38, 49, and 60.
The correct answer is A. 38, 49, 60.