Thread: nth partial sum of a geometric sequence

1. nth partial sum of a geometric sequence

I don't even know if this is an nth partial sum of a geometric sequence problem but...
if someone wanted to save money to buy a used car and they saved $100 on the first day, then$75 on the second day, then $56.25 on the third day, how much will they have saved on the seventh day? In 20 days, will they have enough to afford a used car that costs$500?
what would be the total amount they saved in that time?

thanks

2. Originally Posted by Intsecxtanx
I don't even know if this is an nth partial sum of a geometric sequence problem but...
if someone wanted to save money to buy a used car and they saved $100 on the first day, then$75 on the second day, then $56.25 on the third day, how much will they have saved on the seventh day? In 20 days, will they have enough to afford a used car that costs$500?
what would be the total amount they saved in that time?

thanks
HI

This is a geometric sequence with a=100 , and r =0.75

On the 7th day , they will save $T_7=ar^{n-1}=100(0.75)^{7-1}$

In 20days , they would have saved (in total)

$S_20=\frac{100(1-0.75^{20})}{1-0.75}$

Calculate this and if see whther its > or < 500 .