Question

What is the first term and the common difference of an A.P. recognised as?
A. ’a’ and ‘f’
B. ‘f’ and ‘d’
C. ‘f’ and ‘a’
D. ‘a’ and ‘d’

Answer 1

Hint: To solve this question, we need to have a good idea about the concepts of Arithmetic Progression (A.P). Arithmetic progression is nothing but a series of numbers starting with the first term and such that the difference between any two consecutive numbers is the same. This is sometimes referred to as the common difference of the arithmetic progression. We need to look at the general form of the Arithmetic progression and we can write the solution to the above question.

Complete step by step solution:
We first need to define what an Arithmetic progression (A.P) represents. An arithmetic progression is usually a series of numbers which begins with a number called as the first term and the difference between the consecutive numbers in this series is equal. This means that the consecutive numbers are incremented or decremented by the same number moving forward in the sequence. This same number or difference is known as a common difference.
We represent the Arithmetic progression as follows:
$A.P=a,a+d,a+2d,a+3d,a+4d,\ldots \ldots $
We now write the general equation of an Arithmetic progression:
$A.P={{A}_{n}}=a+\left( n-1 \right)d$
Where, n represents the nth term in the arithmetic progression series.
Here, the first term is given by the term ‘a’ and then the common difference is represented as ‘d’.
Hence the correct answer is given by option D.

Note: Students need a good understanding in the topic of series and sequences. This Arithmetic progression can be found for ‘n’ number of terms, where n can extend up to infinity. Therefore, we can calculate the arithmetic progression for any sequence given the first term and the common difference. These two terms are the most important while defining an A.P.