Question

Find the sum of the first 5 terms of the G.P.
whose first term is 1 and common ratio is 2/3​

Answer 1

HOPE THIS HELPS UUU....

Answer 2

Answer:

$\red {Sum \: of \: 5 \: terms (S_{5})}\green {=\frac{211}{81}}$

Step-by-step explanation:

$Given \: In \: G.P \: first \:term (a) = 1 \\ \: common \:ratio (r) = \frac{2}{3} < 1,\\and \: n = 5$

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

$S_{5} = \frac{ 1\big( 1 - \left(\frac{2}{3}\right)^{5}\big)}{1- \frac{2}{3}}$

$= \frac{ \big( 1 - \frac{32}{243}\big)}{\frac{3-2}{3}}$

$= \frac{\frac{243-32}{243}}{\frac{1}{3}}$

$= \frac{\frac{211}{243}}{\frac{1}{3}}$

$= \frac{211}{243}\times \frac{3}{1}$

$= \frac{211}{81}$

Therefore.,

$\red {Sum \: of \: 5 \: terms (S_{5})}\green {=\frac{211}{81}}$

•••♪