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

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

Answer 2

Answer: 1.05

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* x=x(1+0.05)=1.05x`

Now, the common ratio will be given by :-

`r=(a_(n+1))/(a_(n))`

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

`r=(a_2)/(a_1)=(1.05x)/(x)=1.05`