# How do you determine whether the sequence 4, 7, 10, 13, 16,... is arithmetic and if it is, what is the common difference?

Mar 22, 2018

It is an color(blue)("Arithmetic sequence with ") color(red)("common difference " = 3

#### Explanation:

Sequence is $4 , 7 , 10 , 13 , 16 , . . .$

${a}_{1} = 4 , {a}_{2} = 7 , {a}_{3} = 10 , . . .$

If it is Arithmetic sequence, ${a}_{2} - {a}_{1} = {a}_{3} - {a}_{2} = {a}_{4} - {a}_{3} \text{ & so on }$

In the given sum,

${a}_{2} - {a}_{1} = 7 - 4 = 3$

${a}_{3} - {a}_{2} = 10 - 7 = 3$

${a}_{4} - {a}_{3} = 13 - 10 = 3$

Since the difference between the successive terms is same and

hence $\text{common difference } d = 3$