Question

Determine whether the given sequence is an A.P. 9,16,23,30, …

Answer 1

Hint: In the given question, we are given a sequence of numbers and we need to find whether it forms an arithmetic progression or not. So, in order to check that we need to use the concept of common difference between the terms of the sequence and hence conclude whether it is an arithmetic progression or not.

Complete step-by-step solution:
In the given question, in order to check whether it is an AP or not we need to use the concept of common difference. By common difference we mean the difference between the two consecutive terms. Now, if this difference between two consecutive terms comes out to be the same then we can say that the given sequence of numbers forms an arithmetic progression.
Now, we are given the numbers of the sequence as 9,16,23,30, …
Here, first term is a=9
And second term is 16
So, the difference between two terms is $16-9=7$ ,
Similarly, the difference between next two terms is $23-16=7$ ,
Similarly, the difference between next two terms is $30-23=7$ .
So, clearly, we can see that the difference between the two consecutive terms is the same. Therefore, we can say that the given sequence forms an arithmetic progression.

Note: In this question we need to be careful and be clear with the concept of geometric progression and arithmetic progression and also, we can be asked to find the next terms of the sequence which we can easily find as we know the common difference if it is an arithmetic progression.