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.- 81b.- 27c.81d.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.
Similar Questions
What is the first term of a geometric sequence if its third term is −3 and its sixth term is 81?
Find the 10th term of the arithmetic progression whose 4th term is 7 and whose 17th term is 72.a.42b.47c.32d.37
The sum of the first n terms of the geometric progression, whose first term is 4 and the common ratio is 3, is 4372. Find na.7b.8c.6d.9
Find the nth term of the geometric sequence with given first term a and common ratio r.a = −6, r = −3an = What is the fourth term?a4 =
Which term of the Geometric progression 4, 4√2, 8……64√2 ?a.12b.10c.9d.8
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.