Question

If nth term of a gp is 2^n . The sum of its 6 terms is

Answer 1

$Let \:a \:and \: r \: are \: first \:term \:and \\common \:ratio \: of \:a \:G.P$

$\boxed{\pink { n^{th} \:term (a_{n}) = ar^{n-1}}}$

$\implies a_{n} = 2^{n} \:(given)$

$i ) If \:n = 1 \implies a_{1} = a = 2^{1} = 2$

$ii ) If \:n = 2 \implies a_{2} = 2^{2} = 4$

$Now, Common \:ratio (r) = \frac{a_{2}}{a_{1}}\\= \frac{4}{2}\\= 2$

$\boxed {\pink {Sum \:of \:n\:term (S_{n}) = \frac{a(r^{n}-1)}{(r-1)} }}$

$Sum \:of \:6 \:terms (S_{6}) = \frac{2(2^{6}-1)}{(2-1)} \\= \frac{2(64-1)}{1} \\= 2 \times 63 \\= 126$

Therefore.,

$\red {Sum \:of \:6 \:terms (S_{6})}\green {=126}$

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