Mathematics

How many terms of the series 3, -6, +12, – 24, + ….. are needed…

How many terms of the series 3, -6, +12, – 24, + ….. are needed to make a total of 1-28?
  • A.
    12
  • B.
    10
  • C.
    9
  • D.
    8
Correct Answer: Option C
Explanation

3, -6, +12, -24
a = 3, r = -2
(8n = frac{a(1-r^n)}{1-r}\
∴1-2^8 = frac{3(1-(-2^{n-1}))}{1-(-2)}\
1-2^8 = frac{3(1-(-2^{n-1}))}{3})
1-28 = 1-(-2)n-1
-28 = -2n-1
8 = n-1
n = 9