For a G.P.a=2, r=-2 3 , find S_6 - Vidyadip

Question

For a G.P.$a=2, r=-\frac{2}{3}$, find $S_6$

✓

Answer

$a=2, r=-\frac{2}{3}$
$S_n=\frac{a\left(1-r^n\right)}{1-r}, \text { for } r<1$
$S_6=\frac{2\left[1-\left(-\frac{2}{3}\right)^6\right]}{1-\left(-\frac{2}{3}\right)}$
$ =\frac{2\left[1-\left(\frac{2}{3}\right)^6\right]}{\frac{5}{3}} $
$ =\frac{6}{5}\left[\frac{729-64}{3^6}\right] $
$=\frac{6}{5}\left[\frac{665}{729}\right]$
$S _6 =\frac{266}{243}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Sequences and Series→Sequences and Series — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find: 18th term of the A.P. $\sqrt{2},\ 3\sqrt{2},\ 5\sqrt{2},\ ...$

Find the centre and radius of the circle $x^2+y^2-x+2 y-3=0$.

From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}+\text{b}^\text{x}-2}{\text{x}}$

Find the centre and radius of the circle x = 3 – 4 sin θ, y = 2 – 4 cos θ.

Show that the following points are collinear by determinant method.
$\mathrm{A}(2,5), \mathrm{B}(5,7), \mathrm{C}(8,9)$

A coin is tossed. If it shows tail, we draw a ball from a box which contains $2$ red $3$ black balls; if it shows head, we throw a die.
Find the sample space of this experiment.

Prove that:
$a^{\log _c b}=b^{\log _c a}$

Find the distance of the point A(- 2, 3) from the line 12x – 5y – 13 = 0.

If $a^2=b^3=c^4=d^5$, show that loga $b c d=\frac{47}{30}$.