Question

Find common difference of the following sequence.
 $ 8,15,22,29, \ldots $

Answer 1

Hint: In the given problem, to find a common difference we will find the difference between the consecutive terms of the given sequence. The difference in all pairs of consecutive terms is called the common difference of the sequence.

Complete step-by-step answer:
In this problem, the given sequence is $ 8,15,22,29, \ldots $ . Let us take the difference of the first term $ 8 $ and second term $ 15 $ . So, we get $ 15 - 8 = 7 $ . Hence, we can say that the difference between the first and second term of the sequence is $ 7 $ . Now let us take the difference of the second term $ 15 $ and third term $ 22 $ . So, we get $ 22 - 15 = 7 $ . Hence, we can say that the difference between the second and third term of the sequence is also $ 7 $ . Now let us take the difference of the third term $ 22 $ and fourth term $ 29 $ . So, we get $ 29 - 22 = 7 $ . Hence, we can say that the difference between the third and fourth term of the sequence is also $ 7 $ . If we observe the difference in all pairs of consecutive terms then we can say that the constant difference is $ 7 $ . If the difference in all pairs of consecutive terms of sequence is constant then it is called the common difference of the sequence. Hence, we can say that the common difference of the given sequence is $ 7 $ .

Note: In this problem, we can say that the given sequence is an arithmetic sequence because the difference in all pairs of consecutive terms is equal. The common difference is usually denoted by $ d $ . Also we can say that the given sequence is increasing because the common difference $ 7 $ is positive. Common differences are not always positive. If the common difference is negative then we can say that the sequence is decreasing.