Question

If T21 of an A.P. is zero, then the ratio of T51: 731 will be

Answer 1

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Ratio \ of \ t51:t31 \ is \ 3:1}$

$\sf\orange{Given:}$

$\sf{In \ an \ A.P.}$

$\sf{\implies{t21=0}}$

$\sf\pink{To \ find:}$

$\sf{Ratio \ of \ t15:t31}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{=>tn=a+(n-1)d...formula}$

$\sf{\implies{t21=a+(21-1)d}}$

$\sf{\implies{a+20d=0...(1)}}$

$\sf{\implies{\frac{t51}{t31}=\frac{a+(51-1)d}{a+(31-1)d}}}$

$\sf{\implies{\frac{t51}{t31}=\frac{a+50d}{a+30d}}}$

$\sf{\implies{\frac{t51}{t31}=\frac{a+20d+30d}{a+20d+10d}}}$

$\sf{from \ (1)}$

$\sf{\implies{\frac{t51}{t31}=\frac{0+30d}{0+10d}}}$

$\sf{\implies{\frac{t51}{t31}=\frac{30d}{10d}}}$

$\sf{\implies{\frac{t51}{t31}=\frac{3}{1}}}$

$\sf\purple{\tt{\therefore{Ratio \ of \ t51:t31 \ is \ 3:1}}}$