Arithmetic Sequence: Practice Problems
Direction: Read each arithmetic sequence question carefully, then answer with supporting details.
Work it out first on paper and click “Answer” to compare your solution.
1) Tell whether if the sequence is arithmetic or not. Explain why or why not.
Sequence A : −1, −3, −5, −7, …
Sequence B :−3, 0, 4, 7, …
Sequence A is an arithmetic sequence since every pair of consecutive terms is the same, where the common difference is d= –2.
On the other hand, sequence B is not an arithmetic sequence. There’s no common difference among the pairs of consecutive terms in the sequence.
2) Find the next term in the sequence .
3) Find the next two terms in the sequence .
4) If a sequence has a first term of a1= 12 and a common difference d = −7. Write the formula that describes this sequence.
Use the formula of the arithmetic sequence.
Since we know the values of the first term, a1= 12, and the common difference, d = −7, the only thing we need to do is substitute these values in the formula.
Or, you may further simplify your answer by getting rid of the parenthesis and combining like terms. Both solutions should be acceptable. If you’re not sure, ask your teacher.
5) Write the formula describing the sequence 6, 14, 22, 30, …
6) Find the 45th of the arithmetic sequence −9, −2, 5, 12, …
Find the rule that defines the sequence using the arithmetic sequence formula. The first term is a1= –9 while the common difference is d=7.
Plug these values in the formula, we get
Now we can find the 45th term,
7) Write the formula of a sequence with two given terms, a5= −32 and a18= 85.
Use the information of each term to construct an equation with two unknowns using the arithmetic sequence formula.
- For a5= –32
- For a18=85
Solve the system of equations using the Elimination Method. Multiply Equation # 1 by −1 and add it to Equation #2 to eliminate a1.
After finding the value of the common difference, it is now easy to find the value of the first term. Back substitute d= 9 to any of the two equations to find a1.
We’ll use Equation #1 for this,
Since a1= –68 and d= 9, the formula we’re looking for is,