Question

Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is $62, and then it increases by 4% each month for the rest of the year. Which expression can be used to find the total amount paid in the first 12 months?

Answer 1

Amount paid in first month = $62

Amount paid in second month is 4% more than the first month. So, the amount paid in second month = 62 + 0.04(62) = 1.04(62) = $ 64.48

Similarly, the amount paid in third month will be = 64.48 + 0.04 (64.48) = 1.04(64.48) = $ 67.0592

If we notice the above values we can see that the amounts paid form a geometric sequence with first term 62 and a common ratio of 1.04, as each term is multiplied by 1.04 to get the next term.

The sum of first 12 terms of the sequence will give the total amount paid in the 12 months. Using the formula of sum of Geometric Sequence, we can write:

$S_{n} = \frac{ a_{1}(1-r^{n}) }{1-r}$

Where,
n = number of terms which is 12 in this case
a₁ = First term, which is 62 in this case
r = Common ratio, which is 1.04 in this case.

Using the above expression and the above values we can find the total amount paid in the first 12 months.

Answer 2

Answer:

a1 =50  r = 1.05 n =  12

Step-by-step explanation:

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