Question 22

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Jambmaths question: 

The second term of a geometric series is 4, while the fourth term is 16. Find the sum of the first five terms

Option A: 

54

Option B: 

64

Option C: 

62

Option D: 

60

Jamb Maths Solution: 

$\begin{align}  & {{T}_{n}}=a{{r}^{n-1}} \\ & {{T}_{2}}=a{{r}^{2-1}}=ar=4-----(i) \\ & {{T}_{4}}=a{{r}^{4-1}}=a{{r}^{3}}=16----(ii) \\ & \text{Divide }(ii)\text{ by }(i) \\ & \frac{a{{r}^{3}}}{ar}=\frac{16}{4} \\ & {{r}^{2}}=4 \\ & r=\pm 2 \\ & \text{We assume }r=2\text{     (for our present level)} \\ & {{\text{T}}_{2}}=ar=4 \\ & a\times 2=4 \\ & a=2 \\ & {{S}_{n}}=\frac{a({{r}^{n}}-1)}{r-1} \\ & {{S}_{5}}=\frac{2({{2}^{5}}-1)}{2-1}=\frac{2(32-1)}{1}=62 \\\end{align}$

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