SOLUTION: if a penny is put into a savings account on day one and 2 pennies on day two and so forth until day 100, how much money would be there on day 100? what is the equation for this? T

Algebra ->  Sequences-and-series -> SOLUTION: if a penny is put into a savings account on day one and 2 pennies on day two and so forth until day 100, how much money would be there on day 100? what is the equation for this? T      Log On


   



Question 355160: if a penny is put into a savings account on day one and 2 pennies on day two and so forth until day 100, how much money would be there on day 100? what is the equation for this?
Thanks

Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D=1
a%5B2%5D=2
a%5B3%5D=4
a%5B4%5D=8
.
.
.
a%5Bn%2B1%5D=2%2Aa%5Bn%5D
.
.
.
a%5Bn%2B1%5D=2%5E%28n%29
a%5B100%5D=2%5E99=6.39x10%5E%2829%29
That's a lot of pennies.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
.
*Note: this method of savings describes an arithmetic sequence:
{1,2,3,..100}
.
Sum of n terms of an arithmetic sequence is:
S%5Bn%5D=+%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2
.
S%5B100%5D=+%28100%281+%2B+100%29%29%2F2+=+50%2A101
.
50*101 = 5050 pennies
.
$50.50