Question

In a $AP$, if $d = - 2$, $n = 5$ and ${a_n} = 0$, then the value of $a$ is
A) $10$
B) $5$
C) $ - 8$
D) $8$

Answer 1

Hint:We need the concept of Arithmetic progression to solve this problem .Here all the values which we required to find first term of $AP$ from the formulae of ${n^{th}}$ term is given, So, by putting the given values we can get the answer easily.

Complete step-by-step answer:
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
In the question there is an $AP$ series, whose common difference is $(d) = - 2$ and the number of terms $(n) = 5$ and value of the ${5^{th}}$term $\left( {{a_n}} \right) = 0$. We had to find first term $(a)$, So we use the formulae of term of ${n^{th}}$ an $AP$-
$T_n = a + \left( {n - 1} \right)d$ ; where
$a$ is the first term, $n$ is the no. of term, $d$ is the common difference and $T_n$ is the value of ${n^{th}}$ term.
By putting the values, we get –
${
  0 = a + (5 - 1)( - 2) \\
  or,0 = a - 8 \\
  \therefore a = 8 \\
} $
So, the first term $(a)$ of the given $AP$ is $8$.

So, the correct answer is “Option A”.

Note:This kind of question is very basic of arithmetic progression. You will be able to solve this question by only basic knowledge of finding ${n^{th}}$ term of an $AP$. While solving the equation for ‘a’, do the simple calculations very carefully to avoid silly mistakes. Remember the formulas & concepts of Arithmetic progressions for solving these types of questions.