Question 20

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Jambmaths question: 

The sum to infinity of a geometric progression is $-\tfrac{1}{10}$and the first term is $-\tfrac{1}{8}$.Find the common ratio of the progression.

Option A: 

$-\tfrac{1}{5}$

Option B: 

$-\tfrac{1}{4}$

Option C: 

$-\tfrac{1}{3}$

Option D: 

$-\tfrac{1}{2}$

Jamb Maths Solution: 

$\begin{align}  & a=-\tfrac{1}{8} \\ & {{S}_{\infty }}=-\tfrac{1}{10} \\ & {{S}_{\infty }}=\frac{a}{1-r} \\ & -\frac{1}{10}=\frac{-\tfrac{1}{8}}{1-r} \\ & -\frac{1}{10}=-\frac{1}{8(1-r)} \\ & 8(1-r)=10 \\ & 8-8r=10 \\ & -8r=10-8 \\ & r=-\frac{2}{8} \\ & r=-\frac{1}{4} \\\end{align}$

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