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Consider the given function of an arithmetic sequence:

[tex] f(n) = 7n - 3 [/tex]

What is the 8th term of the sequence?

A. 46
B. 60
C. 67
D. 53

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.

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