Chapter 11, Problem 3SGR

To determine

State whether the statement “The arithmetic means of a sequence are the terms between any two non − successive terms of an arithmetic sequence “is true or false.

Answer to Problem 3SGR

True statement

Explanation of Solution

Given:

The arithmetic means of a sequence are the terms between any two non − successive terms of an arithmetic sequence.

Concept Used:

When three numbers a, A and b are in A.P., then A is called the arithmetic mean of numbers 'a' and 'b'. Given that, $a,\text{A}, b$ is in A.P. Then. As they are in A.P. so their common difference will be constant. $\text{A}-a=d$ and $b -\text{A}=d$ .

The  arithmetic mean  is often known simply as the  mean . It is an average, a measure of the centre of a set of data. The arithmetic mean is calculated by adding up all the values and dividing the sum by the total number of values.

This is true statement.

Thus, this is true statement.