Question

2. Roberto has a wealthy uncle who gives him two options to save money in a bank

account to save for a PlayStation 4, which will cost $518.
Option 1: Roberto's uncle deposits $100 in the first month and $50 for each additional month.
Option 2: Roberto's uncle deposits $5 for the first month and will double the about in the
account each month.
Which option above can be written as a geometric sequence?
A. Option 1
B. Option 2
C. Both Option 1 and 2
D. Neither Option 1 or 2

Answer 1

B. Option 2 (only)

Explanation:

A geometric sequence is a sequence of terms that have a common ratio.

Option 1

The deposits are ...

100, 50, 50, 50, ...

The ratios of terms of this sequence are ...

1/2, 1, 1, 1

So, the ratio is not constant, and the sequence is not geometric.

__

Option 2

The deposits are ...

5, 10, 20, 40, ...

The ratios of terms of this sequence are ...

10/5 = 2, 20/10 = 2, 40/20 = 2, ...

The ratio is constant, so the sequence of deposits for Option 2 is geometric.