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Consider the given function of an arithmetic sequence:

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

What is the [tex]\( 8^{\text{th}} \)[/tex] term of the sequence?

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

Answer :

To find the 8th term of the arithmetic sequence described by the function [tex]\( f(n) = 7n - 3 \)[/tex], we plug in [tex]\( n = 8 \)[/tex] into the function.

Here's a step-by-step approach:

1. Identify the given function: [tex]\( f(n) = 7n - 3 \)[/tex].
2. Substitute [tex]\( n = 8 \)[/tex] into the function to find the 8th term of the sequence:
[tex]\[
f(8) = 7 \times 8 - 3
\][/tex]
3. Perform the multiplication:
[tex]\[
7 \times 8 = 56
\][/tex]
4. Subtract 3 from 56:
[tex]\[
56 - 3 = 53
\][/tex]

So, the 8th term of the sequence is 53. Therefore, the correct answer is:

D. 53

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