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 $12100, how many months will it take Joan to pay back her mortgage?  Pick one:  A) 6  B) 8  C) 10  D) 5  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 12100   This can be re written as :   100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 121   So we have 1 , 3 , 9 , 27 ..... 12100 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   121 = 1 - 3^n / 1-3 ; 1-3^n / -2   Cross multiplying we get   121 x -2 = 1- 3^n   - 242 = 1 - 3^n   - 243 = - 3 ^n   243 = 3 ^n (negatives cancel out)   243 can also be re written as 3 ^ 5   Therefore ; 3 ^5 = 3 ^n   Thus n = 5 (5)
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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 $12100, how many months will it take Joan to pay back her mortgage?