In a geometric progression consisting of real numbers, the 2nd term is 9 and the 6th term is 729. What is the 4th term?a.- 81b.- 27c.81d.27
Question
In a geometric progression consisting of real numbers, the 2nd term is 9 and the 6th term is 729. What is the 4th term?
- a. 81
- b. 27
- c. 81
- d. 27
Solution
In a geometric progression, the ratio of any term to its previous term is constant. Let's denote this ratio as r.
Given that the 2nd term is 9 and the 6th term is 729, we can write the 6th term as:
2nd term * r^(6-2) = 729 9 * r^4 = 729 r^4 = 729 / 9 r^4 = 81 r = 3 (since 3^4 = 81)
Now, to find the 4th term, we can use the 2nd term and multiply it by r^(4-2):
4th term = 2nd term * r^(4-2) 4th term = 9 * 3^2 4th term = 9 * 9 4th term = 81
So, the 4th term of the geometric progression is 81. The correct answer is c. 81.
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