Question 1055333
Two ways to do this.
First is brute force
$20+$40+$80+$160+$320+$640=$1260. She will make it in the 5th month.
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Algebraically
sum of 20*2^(n-1)>=$1200, for n=1 to some number k
factor out a 20 and divide both sides by 20
sum of 2^(n-1), for n=1 to k=60
It is a geometric series where a1=2 and the ratio is 2.
Sum is a1{{1-r^k)/(1-r)}=2(1-r^k)/-1 is greater than = 60
2(1-r^k) is less than or equal to -60
(1-2^k) is <=-30
-2^k <=-31
2^k>=31; k=5