Sheena put $75 down on a new refrigerator. She paid the remaining balance in 18 monthly installments starting with $42.50 in the first month, and then increasing the payments by $10 each month. If the installment plan charged no interest, what is the total amount Sheena paid for the refrigerator at the end of the 18 months?

$4,590

$2,295

$2,370

$3,460

If she increases her monthly payments by 10 each month, then the rate at which it is increasing is in arithmetic progression. The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 18 months

a = $42.50

d = $10

Therefore, the sum of the first 18 terms, S18 would be

S18 = 18/2[2 × 42.5 + (18 - 1)10]

S18 = 9[85 + 170)

S18 = 9 × 255 = $2295

The amount that she paid for the refrigerator the end of the 18 months is

2295 + 75 = $2370