In the formula $a_n = a_1 + (n-1)d$, why is the common difference $d$ multiplied by $(n-1)$ instead of $n$?

Because the common difference is added $n-1$ times to the first term.

Because the sequence must start at term number 0.

Because the first term $a_1$ is always 1.

Because $n$ represents the final value of the sequence.

Arithmetic Sequences Practice — Grade 8 math

Lesson 6: Arithmetic Sequences — Practice Questions

1. What is the 10th term of the arithmetic sequence 5, 11, 17, 23, ...? The answer is ___.
2. Which formula correctly represents the nth term, $a_n$, for the arithmetic sequence 20, 17, 14, 11, ...?
- A. $a_n = 20 - 3n$
- B. $a_n = 23 - 3n$
- C. $a_n = 17 + 3n$
- D. $a_n = 20 + 3n$
3. An arithmetic sequence has a first term of -4 and a common difference of 5. The 12th term is ___.
4. In the formula $a_n = a_1 + (n-1)d$, why is the common difference $d$ multiplied by $(n-1)$ instead of $n$?
- A. Because the common difference is added $n-1$ times to the first term.
- B. Because the sequence must start at term number 0.
- C. Because the first term $a_1$ is always 1.
- D. Because $n$ represents the final value of the sequence.
5. The formula for the nth term of the sequence -2, 2, 6, 10, ... can be written as an expression in terms of $n$. What is this expression? ___
6. An arithmetic sequence has a first term of -2 and a common difference of 5. What is the 15th term of this sequence? ___
7. An arithmetic sequence has a 2nd term of 7 and a 5th term of 16. What is the formula for the general term, $a_n$?
- A. $a_n = 3n + 1$
- B. $a_n = 3n + 4$
- C. $a_n = 4n - 1$
- D. $a_n = 9n - 11$
8. In an arithmetic sequence, the 5th term is 20 and the common difference is -2. What is the 12th term? ___
9. The 3rd term of an arithmetic sequence is 8 and the 7th term is 24. What is the 10th term of the sequence? ___
10. In an arithmetic sequence with first term 3 and common difference 6, which term in the sequence is equal to 63? $n$ = ___