Question

If the $9$th term of an A.P is $35$ and $19$th is $75$, then its $20$th term will be

• A. $78$
• B. $79$
• C. $80$
• D. $81$

Answer 1

The correct option is B $79$

$a_9=a+(9-1)d=a+8d=35$ _________ (1)

and

$a_{19}=a+(19-1)d=a+18d=75$ _________ (2)

$\left(2\right)-\left(1\right)\Rightarrow 10d=40$

$\Rightarrow d=4$

$\therefore a+8\times 4=35$

$\therefore a=35-32$

$\Rightarrow a=3$

$\therefore a_{20}=a+(20-1)d=3+19\times 4$

$=79$