Question

The 11th11th term and the 21st21st term of an A.P. are $16$ and $29$ respectively, then ${34}^{th}$ term is:

• A. $44.6$
• B. $45.9$
• C. $46.5$
• D. $47$

Answer 1

Answer: (B)

$45.9$

Let $a$ and $d$ be the first term and common difference of given AP respectively.
Given $a_{11}=16$ and$a_{21}=29$
$\Rightarrow a+10d=16$ ...(1)
$\Rightarrow a+20d=29$ ...(2)
Subtraction (1) from (2), we get
$10d=13$
$d=\frac{13}{10}$
Putting $d=\frac{13}{10}$ in (1), we get
$a+10\times \frac{13}{10}=16\Rightarrow a=3$
So, $a_{34}=a+33d=3+33\times \frac{13}{10}=45.9$