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------------------------------------------------ Calculate the 42nd term of the arithmetic sequence [tex]\{a_n\} = \{4.5, 2, -0.5, -3, -5.5, \ldots\}[/tex].

A. [tex]-95.5[/tex]
B. [tex]-98[/tex]
C. [tex]-100.5[/tex]
D. [tex]-112[/tex]

To find the 42nd term of the arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence:

[tex]\[ a_n = a_1 + (n - 1) \times d \][/tex]

where [tex]\( a_n \)[/tex] is the nth term, [tex]\( a_1 \)[/tex] is the first term, [tex]\( n \)[/tex] is the term number, and [tex]\( d \)[/tex] is the common difference.

Step 1: Identify the first term ([tex]\( a_1 \)[/tex]) and the common difference ([tex]\( d \)[/tex]) of the sequence.
- The first term [tex]\( a_1 \)[/tex] is 4.5.
- To find the common difference [tex]\( d \)[/tex], subtract the first term from the second term. So, [tex]\( d = 2 - 4.5 = -2.5 \)[/tex].

Step 2: Apply the nth term formula to find the 42nd term.
- We want to find [tex]\( a_{42} \)[/tex], which means [tex]\( n = 42 \)[/tex].

[tex]\[ a_{42} = 4.5 + (42 - 1) \times (-2.5) \][/tex]

Step 3: Simplify the expression.
- Calculate [tex]\( (42 - 1) = 41 \)[/tex].
- Then, multiply by the common difference: [tex]\( 41 \times (-2.5) = -102.5 \)[/tex].
- Add this result to the first term: [tex]\( 4.5 + (-102.5) = -98 \)[/tex].

Therefore, the 42nd term of the sequence is [tex]\(-98\)[/tex]. So, the correct answer is [tex]\(-98\)[/tex].