Question

The ${11}^{th}$ term and the ${21}^{st}$ term of an A.P. are $16$ and $29$ respectively, then the $1^{st}$ term is:

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is B $3$

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)
$a+20d=29$ ...(2)
Subtraction (1) from (2), we get
$10d=13$
$d=\frac{13}{10}=1.3$
Putting $d=\frac{13}{10}$ in (1), we get
$a+10\times \frac{13}{10}=16\Rightarrow a=3$