Question

State the whether given statement is true or false

If the $9^{th}$ term of an $A.P.$ is zero, then show that the ${29}^{th}$ term is twice the ${19}^{th}$ term.

• A. True
• B. False

Answer 1

The correct option is A True

$A.P-a,a+d,........a+(n-1)d$

first term $=a$

common difference $=d$

9th term $=0$

$a+8d=0$

$a=-8d$

29th term $=a+28d$

$=-8d+28d$

$=20d$

19th term $=a+18d$

$=-8+18d$

$=10d$

$\frac{29thterm}{19thterm}=\frac{20d}{10d}=2:1$