Chapter 11, Problem 1MC

To determine

Check whether the given sequence is true or false.

Answer to Problem 1MC

The given sequence is false.

Explanation of Solution

Given data:

The given general term sequence is,

$1,-2,3,-4,\dots$ (1)

The n^th term in the sequence is,

$a_n=n$ (2)

Calculation:

Check that the obtained n^th term may result in given series or not as follows:

Substitute $1$ for $n$ in equation (2) to obtain the first term of the sequence.

$a_1=1$

Substitute $2$ for $n$ in equation (2) to obtain the second term of the sequence.

$a_2=2$

Substitute $3$ for $n$ in equation (2) to obtain the third term of the sequence.

$a_3=3$

Substitute $4$ for $n$ in equation (2) to obtain the fourth term of the sequence.

$a_4=4$

Collect the data obtained by substituting different values for $n$ in $a_n$ and write the series as follows:

$1,2,3,4,\dots$ (3)

Since equation (1) and (3) are not same, the given sequence is false.