Jambmaths question:
The nth term of a sequence is given by ${{2}^{2n-1}}$ . Find the sum of the first four terms.
Option A:
74
Option B:
32
Option C:
42
Option D:
170
Jamb Maths Solution:
$\begin{align} & {{T}_{n}}={{2}^{2n-1}} \\ & {{T}_{1}}={{2}^{2-1}}=2 \\ & {{T}_{2}}={{2}^{2(2)-1}}={{2}^{3}}=8 \\ & r=\frac{{{T}_{2}}}{{{T}_{1}}}=\frac{8}{2}=4 \\ & {{S}_{n}}=\frac{a({{r}^{n}}-1)}{r-1}=\frac{2({{4}^{4}}-1)}{4-1}=\frac{2(255)}{3}=170 \\\end{align}$
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