Chapter 6.5, Problem 63E

To determine

To find:Whether the sequence $10,20,30,\mathrm{40...}$ is arithmetic. If so, what the common difference is.

Answer to Problem 63E

Yes the sequence $10,20,30,\mathrm{40...}$ is arithmetic. The common difference is $10$ .

Explanation of Solution

Given information:The sequence $10,20,30,\mathrm{40...}$

Calculation:A sequence is said to be arithmetic sequence if every term of the sequence, after the first term, is obtained by adding a constant to the preceding term. The constant is known as common difference.

Here, the 1^st term $=10$

Difference between 1^st and 2^nd term $=20-10=10$

Difference between 2^nd and 3^rd term $=30-20=10$

Difference between 3^rd and 4^th term $=40-30=10$

And so on.

Since, each term of the sequence is obtained by adding a constant $10$ to the preceding term, the sequence is arithmetic.

The common difference is $10$ .