Question

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

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

Answer 1

The correct option is B

$7^{th}$

Formula to find $n^{th}$ term of arithmetic progression is

$t_n=a_1+(n-1)d$

where,

'$a_1$' is the first term,

'd' is the common difference,

'n' is the number of terms,

'$t_n$' is the $n^{th}$ term.

Given,

$a_1$ = 12 and d = -2.
Let the term of the AP which is equal to 0 be the $n^{th}$ term .
$\therefore$ $a_1+(n-1)d=0$
$12+(n-1)(-2)=0$
$12+2-2n=0$
$n=7$
Hence, the value of $7^{th}$ term will be 0.