Question

Gr. 11 Pre.Cal HELP ASAP geometric savings after 52 weeks. How much money will Jim have saved in total at the end of the year (a year has 52 weeks?

Jim is saving for money for buying a car. On the first week of his savings, he deposits $1 into an account. On the second week, he deposits $2. On the third week he deposits $4. On week four, he puts in $8. Etc. etc.
How much money will Jim have saved in total at the end of the year (a year has 52 weeks.

Answer 1

`2^52-1`

Explanation:

Jim saving : 1,2,4,8,16...etc.
A year has 52 weeks.`rArrS_n=1+2+4+8+16+...52` times.
So, taking `a=1,r=2/1=4/2=2>1,n=52` ,we get
`S_n=(a(r^n-1))/(r-1)=(1*(2^52-1))/(2-1)=2^52-1`