Question:

In a G.P. the 3rd term is 24 and 6th is 192, then the 10th term is:

Show Hint

In a geometric progression, use the formula \(T_n = a \times r^{n-1}\) to find the \(n\)-th term and solve for unknowns using given terms.
Updated On: May 13, 2025
  • 2072
  • 3072
  • 1072
  • 1672
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

In a geometric progression, the \(n\)-th term is given by: \[ T_n = a \times r^{n-1} \] We are given: - \(T_3 = 24\), so \(a \times r^2 = 24\) - \(T_6 = 192\), so \(a \times r^5 = 192\) Dividing the second equation by the first: \[ \frac{a \times r^5}{a \times r^2} = \frac{192}{24} \quad \Rightarrow \quad r^3 = 8 \] Thus, \(r = 2\). Substituting \(r = 2\) into \(a \times r^2 = 24\): \[ a \times 4 = 24 \quad \Rightarrow \quad a = 6 \] Now, using \(T_{10} = a \times r^9\): \[ T_{10} = 6 \times 2^9 = 6 \times 512 = 3072 \] Thus, the correct answer is option (2).
Was this answer helpful?
5
1