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QuestionKarri deposits \1600initiallyand$300monthly.Findtheformulaforheraccountbalanceatmonth1600 initially and \$300 monthly. Find the formula for her account balance at month n$.

Studdy Solution

STEP 1

Assumptions1. The initial deposit is \1600.Thesameamountofmoneyisdepositedeverymonth3.Thesequencerepresentstheaccountbalanceforthefirstfewmonths$1600,$1900,$2200,…4.Weneedtofindanexplicitformulafortheamountofmoneyinheraccountatthebeginningofmonth1600. The same amount of money is deposited every month3. The sequence represents the account balance for the first few months \$1600, \$1900, \$2200, \ldots4. We need to find an explicit formula for the amount of money in her account at the beginning of month n$

STEP 2

From the given sequence, we can see that the account balance increases by \$300 every month. This means that Karri is depositing \$300 into her account every month after the initial deposit.

STEP 3

We can express the amount of money in the account at the beginning of month nn as the initial deposit plus the total amount deposited in the following months.a(n)=Initial deposit+Monthly deposit×(n−1)a(n) = Initial\, deposit + Monthly\, deposit \times (n-1)

STEP 4

Plug in the values for the initial deposit and the monthly deposit to form the explicit formula.
a(n)=$1600+$300×(n−1)a(n) = \$1600 + \$300 \times (n-1)This is the explicit formula for the amount of money in Karri's account at the beginning of month nn.
Comparing this with the given options, we see that it matches with option C.
So, the correct answer is C. a(n)=1600+(n−1)300a(n)=1600+(n-1)300

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