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

Mathematics
JAMB 2006

How many terms of the series 3, -6, +12, - 24, + ..... are needed to make a total of 1 - 2\(^8\)?

  • A. 12
  • B. 10
  • C. 9
  • D. 8
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Correct Answer: Option D
Explanation

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

There is an explanation video available below.


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