Question

The common ratio of a G.P. is 10. Then the ratio between its 11^th term and its 6^th term is:

• A. \( 10^6 : 1 \)
• B. \( 10^5 : 1 \)
• C. \( 10^4 : 1 \)
• D. \( 10^{11} : 1 \)
• E. \( 10^3 : 1 \)

Hint:

The ratio of the terms of a geometric progression is calculated using the formula \( \frac{T_n}{T_m} = r^{n-m} \).

Answer 1

The Correct Option is B

The \( n \)-th term of a geometric progression is given by: \[ T_n = ar^{n-1} \] where \( a \) is the first term and \( r \) is the common ratio. The ratio between the 11^th term and the 6^th term is: \[ \frac{T_{11}}{T_6} = \frac{ar^{11-1}}{ar^{6-1}} = \frac{r^{10}}{r^{5}} = r^5 \] Given that the common ratio \( r = 10 \), we get: \[ r^5 = 10^5 \] Thus, the ratio is \( 10^5 : 1 \).