SOLUTION: Heather is collecting dimes she saves one dime on the first day two dimes on the second day and three dimes on the third day. If this pattern continues how much money will heather

Question 933471: Heather is collecting dimes she saves one dime on the first day two dimes on the second day and three dimes on the third day. If this pattern continues how much money will heather have saved at the end of 30 days?
a) $45.50
b)$46.00
c)$46.10
d)$46.50
e)$47.50

Would you mind to show me how you got it? Thank you
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You have this arithmetic sequence
1, 2, 3, 4, ..., 28, 29, 30

The first term is 1, the last term is 30. There are 30 terms. So,

a1 = 1
an = 30
n = 30

Use the arithmetic sequence partial sum formula

Sn = n*(a1+an)/2

to get

Sn = n*(a1+an)/2

Sn = n*(1+30)/2

S30 = 30*(1+30)/2

S30 = 465

So she has 465 dimes. Convert to dollars

(465 dimes)*(1 dollar/10 dimes) = 465/10 = 46.50 dollars

So the answer is choice D.
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