# find a general formula for N reductions

• Feb 2nd 2013, 05:22 AM
sergeyrar123
find a general formula for N reductions
Hi,

I want to find what will be left of number X, after 50 reductions of 2% - each time the reference is whats left from the total sum.

I was trying to find a general formula for this but without success.

x - 0.02X - 0.02(x-0.02x) - 0.02(x - 0.02X - 0.02(x-0.02x)) - ..... (N times)

• Feb 2nd 2013, 05:44 AM
earboth
Re: find a general formula for N reductions
Quote:

Originally Posted by sergeyrar123
Hi,

I want to find what will be left of number X, after 50 reductions of 2% - each time the reference is whats left from the total sum.

I was trying to find a general formula for this but without success.

x - 0.02X - 0.02(x-0.02x) - 0.02(x - 0.02X - 0.02(x-0.02x)) - ..... (N times)

1. If you reduce a value by 2% then there is left 98% of the original value.

$\displaystyle N=1 : V = 50 - 50 \cdot \frac2{100} = 50 \cdot \frac{98}{100}$

$\displaystyle N=2 : V = 50 \cdot \frac{98}{100} - 50 \cdot \frac{98}{100} \cdot \frac2{100} = 50 \cdot \frac{98}{100}\cdot \frac{98}{100} = 50 \cdot \left(\frac{98}{100}\right)^2$

$\displaystyle N=3 : V = 50 \cdot \left(\frac{98}{100}\right)^2 - 50 \cdot \left(\frac{98}{100}\right)^2 \cdot \frac2{100} = 50 \cdot \left(\frac{98}{100}\right)^2\cdot \frac{98}{100} = 50 \cdot \left(\frac{98}{100}\right)^3$

... and so on. I guess you see that the 50th reduction of 50 is calculated by:

$\displaystyle V = 50 \cdot (0.98)^{50} \approx 18.21$
• Feb 2nd 2013, 05:48 AM
sergeyrar123
Re: find a general formula for N reductions
YES !!
Thanks alot!