Question

In a GP the 4th term is 8/9 and 7th term is 64/243.find the GP

Answer 1

Hope it helps if so mark as brainliest.

Answer 2

Answer:

The geometric progression is $3,2,\frac{4}{3} ,\frac{8}{9} ,..............$

Step-by-step explanation:

Given that,

The 4th term of the geometric progression is $t_{4}=\frac{8}{9}$ and

The 7th term of the geometric progression is $t_{7}=\frac{64}{243}$

We are required to find the series of geometric progression.

The formula for nth term of the geometric progression is

$t_{n}=ar^{n-1}$

Here a is the first term of the G.P

Based on the above relation,we write the given terms as

$ar^{3}=\frac{8}{9} ---- > (1)\\ar^{6}=\frac{64}{243} ----- > (2)$

Dividing equation (2) with equation (1),we get

$\frac{ar^{6}}{ar^{3}} =\frac{\frac{64}{243} }{\frac{8}{9} } =\frac{9\times64}{243\times8} \\= > r^{3}=\frac{8}{27} = > r=\frac{2}{3}$

The common ratio is obtained as $r=\frac{2}{3}$ now the first term is calculated as follows

$a(\frac{2}{3} )^{3} =\frac{8}{9} = > a=3$

Therefore,the geometric progression is found to be $3,2,\frac{4}{3} ,\frac{8}{9} ,..............$

#SPJ2