|
Question 751047: A father opens a bank account when his daughter is born and deposits $5. Each year on her birthday he deposits twice the amount that he did in the previous year (i.e. on her first birthday he deposits $10). He continues this until she is 16 years old. Assuming that no interest is paid, how much is in the account after this time. This is a nonlinear equation but is also a nonlinear sequence can you help me find the Tn=?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! A father opens a bank account when his daughter is born and deposits $5. Each year on her birthday he deposits twice the amount that he did in the previous year (i.e. on her first birthday he deposits $10). He continues this until she is 16 years old.
5, 10, 20, 40, 80, 160, 320, 640, ....
(x(sub 1))=5 and any element in the sequence is 2(x(sub i -1)) where i = 2,3,...16
we want the summation of x(sub i) where i = 1,2,3,...16
observe that this is a Geometric progression, that is, the quotient of any two successive members of the sequence is a constant
in our sequence we see 10/5 = 2, 20/10 = 2, 40/20=2
for our problem the common ratio (q) is 2 and the scale factor is 5
formula for the sum of the first n numbers of a geometric series is
s(sub n) = x(sub 1) * (1 - q^n) / (1-q)
s(sub 16) = 5 * (1 - 2^16) / (1-2)
s(sub 16) = 5 * (1 - 65536) / (-1)
s(sub 16) = 5 * 65535
s(sub 16) = 327,675
|
|
|
| |
