The $n^{th}$ term of an A.P. having first term 'a' and common difference 'd' is $a_{n}=\_+(n-1)d$,fill in the blank

Question

Accepted Answer

The correct option is 3:
Let's recall the definition of an arithmetic progression (A.P.). An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. This constant difference is called the common difference, denoted by '$d$'. The first term of the A.P. is usually denoted by '$a$'.

The general formula for the $n^{th}$ term of an A.P. is given by:
$a\_n = a + (n-1)d$

In this formula:  * $a\_n$ represents the $n^{th}$ term of the A.P.
  * $a$ represents the first term of the A.P.
  * $n$ represents the position of the term in the sequence.
  * $d$ represents the common difference of the A.P.The question provides the formula as $a_n = _+(n-1)d$ and asks us to fill in the blank. Comparing this with the standard formula $a_n = a + (n-1)d$, it is clear that the blank should be filled with 'a', which represents the first term.

The incorrect option is 1:
Option 'b' is a generic variable and does not represent the first term in the standard notation for an A.P.

The incorrect option is 2:
Option '$\frac{a}{2}$' is half of the first term and is not part of the standard formula for the $n^{th}$ term of an A.P.

The incorrect option is 4:
Option 'n' represents the term number, not the first term of the A.P.