Since it is an arithmetic series, you determine first term (a), the difference in terms (d) and use the sum formula equation for arithmetic series to figure out how many terms there are in the series to produce the value of -66. The first term is 17 / 9. The difference in terms is simplified to -1/3. The sum formula is; (n / 2) [2a + d(n - 1)]. Set this formula equal to -66 and solve for n which is the unknown number of terms that sum to -66. Algebraic manipulation will reduce this to a quadratic equation (-3n^2 + 37n + 1188 = 0) which then yields two root values for n: -44 /3 and 27. Obviously the negative root makes no sense as an 'n' number of terms and thus 27 reflects the number of terms in the series to sum to -66. The last step then is to use the 'nth' term evaluation formula for an arithmetic series to figure out what the final or 27th term (the 'x' term) of the series is. T(n) = a + d(n - 1). Thus the 27th or final term of this series is calculated as: T(27) = (17 / 9) + (-1 / 3) (27 - 1). Number crunching here yields the xth term to be -61 / 9 or -6.7777-----. Cool and tricky problem to come up with since you have to have a whole number of terms for the series (ie 'n' must be a positive integer)
13 mins to solve this simple AP problem? You are bound to fail every exam with such speed. If this was an Olympiad problem both of me and you could succeed in Math Olympiad !! I appreciate your effort to fool others. Put that much effort to solve good problems, everyone will watch your channel regularly including myself.
