Question

Yui makes a list of the balances in her savings account at the end of each month. She notices that each month’s total is 5% greater than the previous month’s total. She writes a recursive formula to describe the account balances.
Which value should she use as the common ratio?

0.05
0.5
1.05
5.0

Answer 1

Answer: 1.05

Step-by-step explanation:

Given: Yui makes a list of the balances in her savings account at the end of each month. She notices that each month’s total is 5% greater than the previous month’s total.

Let the first term be $a_1$=x.

Then the second term will be :-

$a_2=x+5\%\ of\ x=$$x+0.05\times x=x(1+0.05)=1.05x$

Now, the common ratio will be given by :-

$r=\frac{a_{n+1}}{a_{n}}$

Therefore, the common ratio for the given problem will be :-

$r=\frac{a_2}{a_1}=\frac{1.05x}{x}=1.05$

Answer 2

1.05

x + 5%x = x + 0.05x = 1.05x

That will be true each month.

1.05x + 5% (1.05x) = 1.05 x + 0.05(1.05x) = 1.05x(1+1.05) = 1.05[1.05x]

Each month you can multiply the previous amount times the ratio 1.05