Question

finde the ratio of a6 and a8 in the geometric progression √32,√16,√√8.....​

Answer 1

Answer:

2:1

Step-by-step explanation:

by using GP formula it has been done.

a1=√32; a2=√16;a3= √8....

common ratio ,r= (1/√2)

a6= a1.r^(n-1),n = 6

a8= a1.r^(n-1),n = 8

Answer 2

The ratio of $a_6$ and $a_8$ in the G.P. is 2:1.

Step-by-step explanation:

Given : Geometric progression √32,√16,√8.....​

To find : The ratio of $a_6$ and $a_8$ in the G.P. ?

Solution :

Geometric progression $\sqrt{32},\sqrt{16},\sqrt{8},\ ...$

The first term is $a=\sqrt{32}$

The common ratio is $r=\frac{a_2}{a_1}$

$r=\frac{\sqrt{16}}{\sqrt{32}}$

$r=\frac{4}{4\sqrt{2}}$

$r=\frac{1}{\sqrt{2}}$

The sixth term of G.P is $a_6=ar^5$

The eighth term of G.P is $a_8=ar^7$

The ratio of  $a_6$ and $a_8$ is

$a_6: a_8=ar^5:ar^7$

$a_6: a_8=1:r^2$

$a_6: a_8=1:(\frac{1}{\sqrt{2}})^2$

$a_6: a_8=1:\frac{1}{2}$

$a_6: a_8=2:1$

The ratio of $a_6$ and $a_8$ in the G.P. is 2:1.

#Learn more

Determine a3 if an is geometric progression and a4-a2=18 and a5-a3=36

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