# How do you tell whether the sequence 2, -5, -12, -19, -26# is arithmetic?

Jul 17, 2017

Yes, sequence is arithmetic.

#### Explanation:

For a sequence to be arithmetic all consecutive terms must differ by a fixed amount $\left(d\right)$ called the common difference.

Thus if ${a}_{1}$ in the first term, ${a}_{2} = {a}_{1} + d$

In general: ${a}_{n + 1} = {a}_{n} + d \to d = {a}_{n + 1} - {a}_{n}$

In our sequence: $2 , - 5 , - 12 , - 19 , - 26$

${a}_{1} = 2$

${a}_{2} = - 5$

If the sequence is to be arithmetic: $d = - 5 - 2 = - 7$

Testing the next terms in tern:

${a}_{3} = - 5 - 7 = - 12$ Correct

${a}_{4} = - 12 - 7 = - 19$ Correct

${a}_{5} = - 19 - 7 = - 26$ Correct

Since all terms satisify the general condition, the sequence is arithmetic.