Question

If the ${10}^{th}$ term of an $A.P.$ is $35$ and the $5^{th}$ term is $20$, then

• A. $a=9$
• B. $d=3$
• C. $a=8$
• D. $T_9=32$

Answer 1

Answer: (B), (C), (D)

The correct options are
B $d=3$
C $a=8$
D $T_9=32$

Given,
$T_{10}=a+9d=35\cdots \left(i\right)$
$T_5=a+4d=20\cdots \left(ii\right)$
From equation $\left(i\right)$ and $\left(ii\right)$, we get
$\Rightarrow d=3\Rightarrow a=20-12=8$
Now,
$T_9=T_{10}-d=35-3=32$