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.

Answer 1

The recursive formula is f(n + 1) = 1.05f(n)

Answer 2

Answer:

$T_{n}=x(1.05)^{n-1}$

Step-by-step explanation:

Yui makes a list of balances in her savings account at the end of each month.

Each month's total is 5% greater than the previous month's total.

Let the first month's saving is $x.

Then next month's saving will be = x +0.05x

                                                      = (1.05x)

3rd month's saving = 1.05x + 5% of (1.05x)

                                = 1.05x + 0.0525x = 1.1025x

Now the sequence is x, 1.05x, 1.1025x .......

It's a geometric sequence with first term as x and common ratio = 1.05

Explicit formula of a geometric sequence = $ar^{4-1}$

Where a = first term = x

            r = common ratio = 1.05

            x = number of term

So recursive formula will be $T_{n}=x(1.05)^{n-1}$