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

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Answer 1 · 2018-03-22T10:04:58

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

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 " & 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 #"common difference " d = 3#