Question

Find the first term \[a\] and the common difference \[d\] of an A.P.: \[ - 5, - 1,3,7,...\].

Answer 1

Hint: The given question is based on Arithmetic Progression. We can find the first term by looking at the starting point of the AP. It is the starting point of an AP. In order to find the common difference, we can use the formula of difference of any consecutive terms \[d = {T_2} - {T_1}\].

Complete step by step solution:
We are given the first term \[a\] and the common difference \[d\] of an A.P.: \[ - 5, - 1,3,7,...\]
The following terms are important to be noted in case of an Arithmetic Progression:
\[a\]=The first term of an AP from which the sequence begins.
\[d\]=The common difference of an AP. It is obtained by subtracting the second consecutive number from the first number. If \[{T_2}\] and \[{T_1}\] are two terms of an AP, common difference can be found out with the help of following formula:
\[d = {T_2} - {T_1}\]
Let us solve the sum as follows:
On reading the sequence of the Arithmetic Progression, we can make out that the first term \[a\]will be-
\[a = - 5\]
Now the common difference will be difference between any two consecutive terms can be found out with help of formula as follows-
\[d = {T_2} - {T_1} = ( - 1) - ( - 5) = 3 - ( - 1) = 7 - 3 = 4\]
Hence, the first term \[a = - 5\] and the common difference, \[d = 4\].

Note:
A progression or sequence of numbers such that the difference between any two consecutive numbers is constant is called an Arithmetic Progression. An AP may extend infinitely. In order to construct/continue the AP, it is important to know the first term and the common difference. If the common difference is not constant, then the sequence cannot be called an Arithmetic Progression.