Question

The sum of the first and third term of an arithmetic progression is $12$ and the product of first and second term is $24$, then first term is

• A. $1$
• B. $8$
• C. $4$
• D. $6$

Answer 1

The correct option is C

$4$

Explanation for the correct answer:

Let the three consecutive terms in an arithmetic progression be $a-d,a,a+d$.

$\therefore$ $a-d+a+d=12$ …(given)

$\Rightarrow$ $2a=12$

$\Rightarrow$ $a=6$

$\therefore$ $a\left(a-d\right)=24$ …(given)

$\Rightarrow$ $6\left(6-d\right)=24$

$\Rightarrow$ $6-d=4$

$\Rightarrow$ $d=2$

Hence, the first term of the arithmetic progression is $a-d=6-2$

$=4$

Hence, the first term of the arithmetic progression is $4$.

Hence, option C is the correct answer.