document.write( "Question 1055333: If Sarah was saving for a computer that cost$1200 the first month she saved$20 and doubled the amount each month after that how many months will it take her to save the money? \n" ); document.write( "

Algebra.Com's Answer #670565 by Boreal(15235) $\"\"$ $\"About$

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Two ways to do this.
\n" ); document.write( "First is brute force
\n" ); document.write( "$20+$40+$80+$160+$320+$640=$1260. She will make it in the 5th month.
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\n" ); document.write( "Algebraically
\n" ); document.write( "sum of 20*2^(n-1)>=$1200, for n=1 to some number k
\n" ); document.write( "factor out a 20 and divide both sides by 20
\n" ); document.write( "sum of 2^(n-1), for n=1 to k=60
\n" ); document.write( "It is a geometric series where a1=2 and the ratio is 2.
\n" ); document.write( "Sum is a1{{1-r^k)/(1-r)}=2(1-r^k)/-1 is greater than = 60
\n" ); document.write( "2(1-r^k) is less than or equal to -60
\n" ); document.write( "(1-2^k) is <=-30
\n" ); document.write( "-2^k <=-31
\n" ); document.write( "2^k>=31; k=5
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