Question

If $9^{th}$ and ${19}^{th}$ terms of an AP are $35$ and $75$, then its ${20}^{th}$ term is

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

Answer 1

Answer: (B)

$79$

$T_9=35\Rightarrow a+(9-1)d=35\Rightarrow a+8d=35$

$T_{19}=75\Rightarrow a+(19-1)d=75\Rightarrow a+18d=75$

Solving these two we get
$d=4,a=3$

Therefore,
$T_{20}=a+(20-1)d=3+19\times 4=79$