Question 27

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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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