Options:
a. 2.5, 6.25, 15.625, 39.0625, …
b. 2.5, 5, 10, 20
c. -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
Answer:
C. –10, –7.5, –5, –2.5, …
Step-by-step explanation:
Given
f(n+1) = f(n) + 2.5 where n ≥ 1
Required
Which sequence partially defines the function
This question will be tackled using a trial and error approach (we’ll evaluate each option provided)
Let’s consider f(1) as the starting point for each sequence since n >= 1.
A.
2.5, 6.25, 15.625, 39.0625, …
f(1) = 2.5
f(n+1) = f(n) + 2.5
So when n = 1
f(2) = f(1) + 2.5 = 5
This option does not define the sequence.
B.
2.5, 5, 10, 20
f(1) = 2.5
So when n = 1
f(2) = f(1) + 2.5 = 5
For n = 2
f(3) = f(2) + 2.5 = 7.5
This option also does not define the sequence.
C.
-10, -7.5, -5, -2.5, …
f(1) = -10
So when n = 1
f(2) = f(1) + 2.5 = -7.5
For n = 2
f(3) = f(2) + 2.5 = -5
For n = 3
f(4) = f(3) + 2.5 = -2.5
This defines the function, so there’s no need to assess D.
