Question

Tell whether the sequence of y-values is arithmetic or geometric. Then, find y when n = 5.

A: arithmetic; When n = 5, y = 30.
B: arithmetic; When n = 5, y = 7776.
C: geometric; When n = 5, y = 7776.
D: geometric; When n = 5, y = 30.

Answer 1

C: geometric; When n = 5, y = 7776

Explanation:

See the attached table.

We can see that the value of y increases quickly for each +1 increase in n. Y goes from 6 to 1296 with an increase of n of 1 to 4. This strongly suggests a geometric increase. If we write a few possible functions, we are able to quickly establish the more likely type of function. All we know is that y is a function of n, or y = f(n). Since y = 6 when n = 1, lets write a few functions that would meet this requirement [f(1) = 6]:

a) y = 5 + n

b) y = 5n + 1

c) y = 6^n

All three result in y = 6 when n = 1. The first two (a and b) are arithmetic. The third is geometric.

But when we try n = 2, we quickly find that a and b both fail. The results for all three functions at n = 2 are:

a) 7

b) 11

c) 36

Function c matches the given result of 36. A and b both fail.

If we continue with higher values of n, we find that function c always gives the correct result. See the table. By using n = 5, we obtain the value of 7776 (green cell), which is the value requested in the problem. The sequence is geometric and results in 7776 when n = 5.