The 4th term of a geometric progression is 2÷3 and the 7th term is 16÷81.Find the geometric series.
Answers
Answered by
28
Answer see in image
The g. P. Is 9/4,3/2,1,2/3----
The g. P. Is 9/4,3/2,1,2/3----
Attachments:
anjalijugral:
thanku
welcome
you done this answer for me
so thanks
its my pleasure
Answered by
21
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 ...
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 ...
Similar questions