Question on Geometric Progression

Topic : Geometric Progression

Question : If your allowance was a penny doubled every day, how many days would it take for you to have over $1000.00? On which day would you have over $10000.00? How much money would you have on the 15th day?

Answer :
Since the allowance starts from a penny u have to consider the
G.P {1,2,4,8,16,....) for this.

Sum to n terms of the G.P. = a(r^n - 1)/(r-1) = 2^n -1

now for the first question 2^n - 1 ≥ 100000

this gives the value of n to be 17.

For the second question 2^n - 1 ≥ 1000000
for which n = 20

For the third question total amount on the 15th day = 2^15 - 1 pennies
= $327.67

Hope the explanation in the answer will help you to solve similar kind of problems in progression.