Chapter 6.5, Problem 60E

To determine

To find: Whether the sequence $-20,-26,-32,-\mathrm{38...}$ is arithmetic. If so, what the common difference is.

Answer to Problem 60E

Yes the sequence $-20,-26,-32,-\mathrm{38...}$ is arithmetic. The common difference is $-6$ .

Explanation of Solution

Given information: The sequence $-20,-26,-32,-\mathrm{38...}$

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 $=-20$

Difference between 1^st and 2^nd term $=-26-(-20)=-20+20=-6$

Difference between 2^nd and 3^rd term $=-32-(-26)=-32+26=-6$

Difference between 3^rd and 4^th term $=-38-(-32)=-38+32=-6$

And so on.

Since, each term of the sequence is obtained by adding a constant $-6$ to the preceding term, the sequence is arithmetic.

The common difference is $-6$ .