Question

5) For a G.P. If a = 3 and t^7= 192 find r and t^11.​

Answer 1

$\huge\star\underline\mathfrak\red{Answer:-}$

Refer to the attachment above for your answer!!

Thank you!!

Answer 2

Given:

For a Geometric progression, the value of a is 3. The value of t7 is 192.

To Find:

The common ratio and the value of t11.

Solution:

1. Consider a G.P with first term a and common ratio r. The nth term of a G.P is given by the formula,

=> nth term =$t_{n} = ar^{n-1}$.

2. The value of a is 3. The value of the 7th term is 192. Hence,

=> t7 = ar^6 = 192,

=> 3r^6 = 192,

=> r^6 = 64,

=> r^6 = 2^6,

=> r = 2.

=> Common ratio = 2.

3. The value of t11 is,

=> t11 = a*(r^10),

=> t11 = 3*(2^10),

=> t11 = 3(1024),

=> t11 = 3072.

Therefore, the value of r and t11 are 2 and 3072 respectively.