Question

the first term of a geometric series is -1, and the common ratio is -3. How many terms are in the series if its sum is 182?

Answer 1

-1 +3 -9 +27......+-3^(n-2) + 3^(n-1)
3(1+9+27....3^(n-2)) -1(1+3+9+...3^(n-2)) =2(1+9+27+...3^(n-2)) = 182
=> 1+9+....9^[(n-2)/2] = 91
=>( 9^(n/2) -1)/(9-1) = 91
=>3^n - 1 =728
=>3^n = 729
=>n=6