The 4th term of a geometric progression is 2÷3 and the 7th term is 16÷81.Find th...

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juveria11 @juveria11

July 2022 2 57 Report

The 4th term of a geometric progression is 2÷3 and the 7th term is 16÷81.Find the geometric series.

anjalijugral

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The g. P. Is 9/4,3/2,1,2/3----

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HappiestWriter012

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We know that nth term of a geometric progression is a*r^n-1 .

Now fourth term = ar³ =2/3

Seventh term = ar^6 = 16/81

Dividing the above, we get

r³ = 16/81 ÷ 2/3

r³ = 16/81 * 3/2

r³ = 8/27

r = 2/3 .

Now, ar³ = 2/3

a = 2/3 ÷ 8/27

a = 2/3 * 27/8 = 9/4 .

ar = 9/4(2/3) = 3/2

ar² = 9/4(4/9) = 1

ar³ = 2/3

Therefore, the geometric progression is as follows :- 9/4 , 3/2 , 1 ,2/3 ...

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