Question

If fourth term of an A.P. is zero, then $\frac{t_{25}}{t_{11}}$ is, where $t_n$ denotes the $n^{\text{th }}$ term of AP.

• (A) 2
• (B) 3
• (C) 4
• (D) 5

Answer 1

The Correct Option is B

Explanation:
Let the first term of AP be 'a' and the common difference be 'd'.Given: Fourth term of an A.P. is zero.$\Rightarrow {\mathrm{a}}_4=0$$n^{\text{th }}$ term of the A.P. is given by $a_n=a+(n-1)d$$\Rightarrow \mathrm{a}+(4-1)\times \mathrm{d}=0$$\Rightarrow \mathrm{a}+3\mathrm{d}=0$$\therefore \mathrm{a}=-3\mathrm{d}$To Find: $\frac{{\mathrm{t}}_{25}}{{\mathrm{t}}_{11}}$$\Rightarrow \frac{{\mathrm{t}}_{25}}{{\mathrm{t}}_{11}}=\frac{\mathrm{a}+24\mathrm{d}}{\mathrm{a}+10\mathrm{d}}$$\Rightarrow \frac{{\mathrm{t}}_{25}}{{\mathrm{t}}_{11}}=\frac{-3d+24d}{-3d+10d}$$\Rightarrow \frac{{\mathrm{t}}_{25}}{{\mathrm{t}}_{11}}=\frac{21\mathrm{d}}{7\mathrm{d}}$$\Rightarrow \frac{{\mathrm{t}}_{25}}{{\mathrm{t}}_{11}}=3$Hence, the correct option is (B).