Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $914800, how many months will it take Joan to pay back her mortgage?
Choose the correct answer.
A) 6
B) 8
C) 10
D) 9
E) 13
Joan starts off with 100 $ .. which is to be tripled every month   Her monthly payments look like this :   100 , 300 , 900 , 2700 ......... Upto 914800   This can be re written as :   100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 9148   So we have 1 , 3 , 9 , 27 ..... 914800 in GP   We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)   Therefore to find the Sum of n terms of a GP we use this formula :   Sn = a (1-r^n) / 1 -r   Using this and plugging in the information we get ...   9148 = 1 - 3^n / 1-3 ; 1-3^n / -2   Cross multiplying we get   9148 x -2 = 1- 3^n   - 19682 = 1 - 3^n   - 19682 = - 3 ^n   19683 = 3 ^n (negatives cancel out)   19863 can also be re written as 3 ^ 9   Therefore ; 3 ^9 = 3 ^n   Thus n = 9 (9)
<result>D</result>
Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $914800, how many months will it take Joan to pay back her mortgage?