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? Choose the correct choice from the following options:  A) 6  B) 8  C) 10  D) 5  E) 13

Rationale: "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 = a 3 ^ 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 ( d )"
Answer: D