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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

Verified Answer :

Edufirst

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

JeanaShupp

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 :-

\(r=\frac{a_2}{a_1}=\frac{1.05x}{x}=1.05\)

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