Question

A school district purchases new laptops. The number of classrooms using the laptops each month is modeled by

a
n
=
5
(
1.6
)
n
−
1
for natural numbers n.


A student claims that this function represents the same sequence as the recursive model

a
1
=
8,

a
n
=
1.6
⋅
a
n
−
1
​


Is the student correct?



A.
Yes, because both use a growth factor of 1.6.

B.
Yes, because both are increasing exponential functions.

C.
No, because the starting values differ, so the sequences will not match.

D.
No, because the starting values differ, so the sequences will not match.

Answer 1

C. No, because the starting values differ, so the sequences will not match.

Explanation: For the explicit formula a1 = 5·(1.6)^{0} = 5, but the recursive model has a1 = 8. With different initial terms the geometric sequences are not the same (they are a shift of each other).