College

Select the correct answer.

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. 46
B. 67
C. 53
D. 60

Answer :

To find the 8th term of the arithmetic sequence defined by the function [tex]\( f(n) = 7n - 3 \)[/tex], follow these steps:

1. Identify the position: We are asked to find the 8th term of the sequence, so [tex]\( n = 8 \)[/tex].

2. Substitute [tex]\( n \)[/tex] into the function: Replace [tex]\( n \)[/tex] with 8 in the function [tex]\( f(n) = 7n - 3 \)[/tex]:
[tex]\[
f(8) = 7 \cdot 8 - 3
\][/tex]

3. Perform the multiplication: Calculate [tex]\( 7 \cdot 8 \)[/tex]:
[tex]\[
7 \cdot 8 = 56
\][/tex]

4. Subtract 3: From the result of the multiplication, subtract 3:
[tex]\[
56 - 3 = 53
\][/tex]

Thus, the 8th term of the sequence is [tex]\( 53 \)[/tex].

The correct answer is:
C. 53

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