Question

for a G. P. if a=3 and ty = 192 find r and t11​

Answer 1

Answer:

• r = 2
• t_11 = 3072

Step-by-step explanation:

Correct Question :-

For a G.P , If a = 3 and t_7 = 192, find r and t_11

Given,

First term of a G.P(a) = 3

nth term of a G.P = 192

To Find :

Common difference (r) and t_11

Solution :-

We know that nth term of G.P :-

$a_n = a \times {r}^{n - 1}$

According to Question

t_n = t_7

$\implies \: n = 7$

$192 = 3 \times {r}^{7 - 1}$

$192 = 3 \times {r}^{6}$

$\dfrac{192}{3} = {r}^{6}$

$64 = {r}^{6}$

${r}^{6} = {2}^{6}$

Since, 64 = 2^6

Applying 6th root on both sides :-

$\sqrt[6]{ {r}^{6} } = \sqrt[6]{ {2}^{6} }$

r = 2

Since, Common Difference = r = 2.

$t_{11} = 3 \times {2}^{11 - 1}$

$= 3 \times {2}^{10}$

$= 3 \times 1024$

= 3072

Since , t_11 = 3072.