Chapter 8, Problem 1MC

Determine whether the statement is true or false.

1. The general term of the sequence 1, −2, 3, −4, . . . can be expressed as a_n = n. [8.1]

To determine

Check whether the given statement is true or false.

Answer to Problem 1MC

The given statement is false.

Explanation of Solution

Given:

The given statement is “The general term of the sequence $1,-2,3,-4,\dots$ can be expressed as $a_n=n$.”

Calculation:

The given general term sequence is,

$1,-2,3,-4,\dots$        (1)

The n^th term in the sequence is,

$a_n=n$        (2)

Check whether 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 sequence (1) and (3) are not same, the given statement is false.