Question

In a h.p. if 5th term is 6 and 3rd term is 10 . find the 2nd term

Answer 1

Answer:

$T_2=15$

Step-by-step explanation:

Formula used:

n th term of H.P is

$T_n=\frac{1}{a+(n-1)d}$

Given:

$T_5=6$

$T_5=\frac{1}{a+4d}$

$6=\frac{1}{a+4d}$

$a+4d=\frac{1}{6}$.........(1)

$T_3=10$

$T_3=\frac{1}{a+2d}$

$10=\frac{1}{a+2d}$

$a+2d=\frac{1}{10}$.........(2)

(1)-(2)==>

$2d=\frac{1}{6}-\frac{1}{10}$

$2d=\frac{10-6}{60}$

$2d=\frac{4}{60}$

$d=\frac{2}{60}$

$d=\frac{1}{30}$

put $d=\frac{1}{30}$ in (2)

$a+2(\frac{1}{30})=\frac{1}{10}$

$a+(\frac{2}{30})=\frac{1}{10}$

$a=\frac{1}{10}-\frac{2}{30}$

$a=\frac{3}{30}-\frac{2}{30}$

$a=\frac{1}{30}$

$\implies\:a+d=\frac{1}{30}+\frac{1}{30}=\frac{2}{30}=\frac{1}{15}$

Now,

$T_2=\frac{1}{a+d}$

$T_2=15$