Jambmaths question:
How many terms of the series 3 – 6 + 12 – 24 + - - - are needed to make a total 1 – 28
Option A:
9
Option B:
12
Option C:
8
Option D:
10
Jamb Maths Solution:
$\begin{align} & a=3,r=-2 \\ & {{S}_{n}}=\frac{a(1-{{r}^{n}})}{1-r} \\ & 1-{{2}^{8}}=\frac{3\left[ 1-{{(-2)}^{n}} \right]}{1-(-2)} \\ & 1-{{2}^{8}}=\frac{3\left[ 1-{{(-2)}^{n}} \right]}{3} \\ & 1-{{2}^{8}}=1-{{(-2)}^{n}} \\ & -{{2}^{8}}=-{{(-2)}^{n}} \\ & \text{Since }8\text{ is even, we ignore the negative signs} \\ & n=8 \\\end{align}$
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