Which recursive formula describes the arithmetic sequence $5, 11, 17, 23, ...$?

$a_1 = 5$ and $a_n = a_{n-1} + 6$

$a_1 = 6$ and $a_n = a_{n-1} + 5$

$a_1 = 5$ and $a_n = a_{n-1} - 6$

$a_1 = 5$ and $a_n = a_{n-1} + 5$

Which recursive formula correctly represents the sequence $20, 15, 10, 5, ...$?

$a_1 = 20$ and $a_n = a_{n-1} + 5$

$a_1 = 5$ and $a_n = a_{n-1} - 20$

$a_1 = 20$ and $a_n = a_{n-1} - 5$

$a_1 = 20$ and $a_n = a_{n-1} + (-20)$

Arithmetic Sequences Practice — Grade 11 math

Lesson 4: Arithmetic Sequences — Practice Questions

1. Which recursive formula describes the arithmetic sequence $5, 11, 17, 23, ...$?
- A. $a_1 = 5$ and $a_n = a_{n-1} + 6$
- B. $a_1 = 6$ and $a_n = a_{n-1} + 5$
- C. $a_1 = 5$ and $a_n = a_{n-1} - 6$
- D. $a_1 = 5$ and $a_n = a_{n-1} + 5$
2. An arithmetic sequence is defined by the recursive formula $a_1 = 10$ and $a_n = a_{n-1} - 4$. What is the value of the third term, $a_3$? $a_3$ = ___
3. Which recursive formula correctly represents the sequence $20, 15, 10, 5, ...$?
- A. $a_1 = 20$ and $a_n = a_{n-1} + 5$
- B. $a_1 = 5$ and $a_n = a_{n-1} - 20$
- C. $a_1 = 20$ and $a_n = a_{n-1} - 5$
- D. $a_1 = 20$ and $a_n = a_{n-1} + (-20)$
4. For the arithmetic sequence $-8, -5, -2, 1, ...$, what is the common difference $d$ used in the recursive formula $a_n = a_{n-1} + d$? $d$ = ___
5. An arithmetic sequence has the recursive formula $a_1 = -1$ and $a_n = a_{n-1} + 5$. What is the value of the fourth term, $a_4$? $a_4$ = ___
6. An arithmetic sequence is defined by the recursive formula $a_1 = 7$ and $a_n = a_{n-1} + 2$. What is the explicit formula for this sequence? $a_n = $___
7. Which recursive formula correctly represents the arithmetic sequence defined by the explicit formula $a_n = 6n - 4$?
- A. $a_1 = 2$, $a_n = a_{n-1} + 6$
- B. $a_1 = 6$, $a_n = a_{n-1} + 2$
- C. $a_1 = -4$, $a_n = a_{n-1} + 6$
- D. $a_1 = 2$, $a_n = a_{n-1} - 4$
8. Given the recursive definition $a_1 = 10$ and $a_n = a_{n-1} - 4$ for an arithmetic sequence, find the explicit formula. $a_n = $___
9. An arithmetic sequence is given by the explicit formula $a_n = -5n + 8$. Which of the following is the correct recursive definition for this sequence?
- A. $a_1 = 3$, $a_n = a_{n-1} - 5$
- B. $a_1 = 8$, $a_n = a_{n-1} - 5$
- C. $a_1 = 3$, $a_n = a_{n-1} + 8$
- D. $a_1 = -5$, $a_n = a_{n-1} + 3$
10. An arithmetic sequence is described by the explicit formula $a_n = 7n - 3$. If this sequence were written in recursive form, what would be the value of the first term, $a_1$? $a_1 = $___