The 6th term of a geometric series falls between 4090 and 5010. What could possibly be the first term of the series if the first term and common ratio are equal?
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A geometric progression with first term a and common ratio r is given as : a, ar, ar², ar³, ar�, ar�, ar�...varun289 wrote:The 6th term of a geometric series falls between 4090 and 5010. What could possibly be the first term of the series if the first term and common ratio are equal?
So, 6th term = ar�
Here, a = r
Hence, 6th term = a*(a�) = a�
So, 4090 < a� < 5010
--> 3600 < a� < 6400
--> 60 < a³ < 80
Check the options...
- A. a = 3 ---> a³ = 3³ = 27 < 60 --> NO
B. a = 4 ---> a³ = 4³ = 64 ---> 60 < 64 < 80 --> YES
C. a = 5 ---> a³ = 5³ = 125 > 80 --> NO
No need to check the rest as they are greater than 5.
