Question

The first term of an AP is 12 and the common difference is -2. Which term of the AP will be 0?

• A. $6^{\text{th}}$
• B. $7^{\text{th}}$
• C. ${10}^{\text{th}}$
• D. ${12}^{\text{th}}$

Answer 1

The correct option is B $7^{\text{th}}$

Let $a$ be the first term of an AP and $d$ be its common difference.
Then, $a=12$ and $d=-2.$
Let $a_n$ be the term of the AP that equals zero.

i.e., $a_n=0$
Since the $n^{\text{th}}$ term of the AP is given by $a_n=a+(n-1)d,$
we have $a+(n-1)d=0$
i.e., $12+(n-1)(-2)=0$
$⟹12+2-2n=0$
$⟹n=7$
Thus, the $7^{\text{th}}$ term equals zero.