Question

In a geometric progression the 4 term is 8 and the 8 term is 128/625.find the geometric progression

Answer 1

Answer:

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Answer 2

The geometric progression are 125, 50, 20,.....

Step-by-step explanation:

Let the first term = a and common ratio = r

To find, the geometric progression = ?

We know that,

The nth term of GP,

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

$a_{4}=ar^{4-1}$

⇒ $ar^{3}$ = 8         ....... (1)

Also,

$ar^{8-1}$ = $\dfrac{128}{625}$

⇒ $ar^{7}$ = $\dfrac{128}{625}$

Using equation (1), we get

$(ar^{3})r^{4}$ = $\dfrac{128}{625}$

⇒ $(8)r^{4}$ = $\dfrac{128}{625}$

⇒ $r^4=\dfrac{16}{625} =(\dfrac{2}{5} )^4$

⇒ r = $\dfrac{2}{5}$

Putting the value of r in equation (1), we get

$a(\dfrac{2}{5})^{3}$ = 8

⇒ $a\dfrac{8}{125}$ = 8

⇒ a = 125

∴ The geometric progression are:

a, ar, a$r^{2},$

= 125, 50, 20,....

Thus, the geometric progression are 125, 50, 20,.....