Answer :
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].
[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].
