Question

You save ​$1 the first day of the​ month, ​$2 the second​ day, ​$4 the third​ day, continuing to double your savings each day. what will your savings be for the first 15 ​days?

Answer 1

Try this solution:
1. In order to calculate the total sum for the first 15 days, it need to calculate the sum of the first 15 terms of the geometric sequence: 1; 2; 4; 8; 16;... etc.2. using the formula (a₁=1; q=2; n=15):
`S= (a_1*q^n-a_1)/(q-1)`
`S= (1*2^(15)-1)/(2-1)=2^(15)-1=32768-1=32767`
answer: 32767 $