Chapter 12.2, Problem 3E

To determine

Find whether the statement is true or false.

Answer to Problem 3E

The statement is true.

Explanation of Solution

Given:

It is given in the question that the statement is the nth partial sum of an arithmetic sequence is the average of the first and last terms times n .

Since, nth partial sum of arithmetic sequence is : $S_n=n(\frac{a_1+a_n}{2})$

For example : Let the arithmetic sequence be : $1,3,5,7,9,11,13,\mathrm{15............}$

Sum of first $4$ terms : $S_4=4(\frac{1+7}{2})=4\times 4=16$ .

Now calculating the sum by adding : $1+3+5+7=16$ .

Hence, the given statement nth partial sum of an arithmetic sequence is the average of the first and last terms times n is true.