Answer :
To find the [tex]\(8\)[/tex]th term of the given arithmetic sequence, we can use the formula for the function:
[tex]\[ f(n) = 7n - 3 \][/tex]
Step 1: Identify the term number
- We need the [tex]\(8\)[/tex]th term, so [tex]\( n = 8 \)[/tex].
Step 2: Substitute [tex]\( n = 8 \)[/tex] into the function
- Replace [tex]\( n \)[/tex] in the formula with [tex]\( 8 \)[/tex]:
[tex]\[ f(8) = 7(8) - 3 \][/tex]
Step 3: Perform the multiplication
- First, calculate [tex]\( 7 \times 8 \)[/tex]:
[tex]\[ 7 \times 8 = 56 \][/tex]
Step 4: Subtract 3
- Now subtract [tex]\( 3 \)[/tex] from [tex]\( 56 \)[/tex]:
[tex]\[ 56 - 3 = 53 \][/tex]
Thus, the [tex]\(8\)[/tex]th term of the sequence is [tex]\(53\)[/tex].
Therefore, the correct answer is D. 53.
[tex]\[ f(n) = 7n - 3 \][/tex]
Step 1: Identify the term number
- We need the [tex]\(8\)[/tex]th term, so [tex]\( n = 8 \)[/tex].
Step 2: Substitute [tex]\( n = 8 \)[/tex] into the function
- Replace [tex]\( n \)[/tex] in the formula with [tex]\( 8 \)[/tex]:
[tex]\[ f(8) = 7(8) - 3 \][/tex]
Step 3: Perform the multiplication
- First, calculate [tex]\( 7 \times 8 \)[/tex]:
[tex]\[ 7 \times 8 = 56 \][/tex]
Step 4: Subtract 3
- Now subtract [tex]\( 3 \)[/tex] from [tex]\( 56 \)[/tex]:
[tex]\[ 56 - 3 = 53 \][/tex]
Thus, the [tex]\(8\)[/tex]th term of the sequence is [tex]\(53\)[/tex].
Therefore, the correct answer is D. 53.