Answer:
Having a nickel doubled for 10 days gives 512 nickels, or 2560 cents.
Step-by-step explanation:
Having a nickel doubled in value each day for 10 days, we first write the amount of nickels we have in the first few days, inspect what pattern these numbers take, write a general formula for the sequence formed, and use the formula to find the 10th number easily.
For the first five days we have:
Day1: 1
Day2: 1 + 1 = 2
Day 3: 2 + 2 = 4
Day 4: 4 + 4 = 8
Day 5: = 8 + 8 = 16
...
This is a geometric progression, where the first term is 1, and the common ratio is 2.
The nth term is given as
Tn = ar^(n - 1)
Tn = 1 × 2^(n - 1)
= 2^(n - 1)
That is
Day n = 2^(n - 1)
Day 10 = 2^(10 - 1) = 2^9 = 512 nickels.
But because 1 nickels = 5 cents
512 nickels = 5 × 512 = 2560 cents.
