Answer:
The 10th term in the geometric progression is 29.
Step-by-step explanation:
Given: In a geometric series, [T3 = 18] and [T6 = 486].
To find: The term [T10]?
Solution:
A geometric sequence takes the form [a, ar, ar^2,...]
Where, a represents the first term, and r denotes the common ratio.
The nth term is expressed as [Tn = a * r^(n-1)]
From the information provided: [T3 = a * r^2 = 18]
And [T6 = a * r^5 = 486]
By dividing the second equation by the first:
[(a * r^5) / (a * r^2)] = 486 / 18
[r^3 = 27]
Taking the cube root provides: r = 3.
Inserting r into one of the equations allows us to solve for a.
Substituting r gives: [T3 = a * r^2 = 18]
Thus, the first term is a = 2, and the common ratio is r = 3.
The 10th term in the geometric progression is computed as:
[T10 = a * r^(10-1)]
[Thus, T10 = 29.]
