Problema Solution
2. Tom adds 5 pennies to his penny collection each day.
a) How could you change the above scenario to make it a geometric series rather than an arithmetic series?
b) Using you geometric series from part a, how many pennies would Tom have in total after 10 days? Show all work to receive full credit.
Answer provided by our tutors
We can make geometric series by stating "Tom increases his penny collection 5 times each day"
Assuming Tom starts with 1 penny per day:
a1 = 1
a2 = 5*a0
an = 5^(n-1)*a1
We need to find the sum of the first n members of the geometric series:
Sn = a1(1 - r^n)/(1 - r)
In our case a1 = 1, r = 5, n = 10
S10 = 1*(1 - 5^10)/(1 - 5)
S10 = 2,441,406 pennies
After 10 days Tom will have 2,441,406 pennies.