What is the next number in the sequence: 5, 11, 17, 23, ___?
A27, because you add 4 each time
B29, because you add 6 each time
C30, because 23 + 7 = 30
D28, because you add 5 each time
To find the rule, check the gap between consecutive terms: 11 − 5 = 6, 17 − 11 = 6, 23 − 17 = 6. The common difference is 6. The next term is 23 + 6 = 29. The wrong answers (4, 5, 7) come from only partially checking — perhaps eyeballing one pair of terms. Verifying the gap across multiple consecutive pairs is essential before trusting any rule.
Question 2 Multiple Choice
A student wants to find the 7th term of the sequence 3, 8, 13, 18, 23... Which approach is most efficient?
AContinue the sequence one step at a time: 28, 33, and that's the 7th term
BUse multiplication: the 7th term = 3 + (6 × 5) = 33
CThe 7th term cannot be found without writing the whole sequence first
DMultiply 7 × 5 = 35
For any arithmetic sequence, the nth term = first term + (n − 1) × common difference. For the 7th term: 3 + (7 − 1) × 5 = 3 + 30 = 33. This is faster than hopping forward step by step. Option D (7 × 5 = 35) forgets to add the starting value of 3. This connection to multiplication is the key — once you know the common difference, you can jump to any term without stepping through all the ones in between.
Question 3 True / False
The sequence 4, 8, 12, 16, 20 is the same as the multiplication table for 4.
TTrue
FFalse
Answer: True
An arithmetic sequence starting at 4 with a common difference of 4 produces exactly the multiples of 4: 4×1=4, 4×2=8, 4×3=12, and so on. This connection means you can find any term in the sequence using multiplication instead of counting forward step by step. Recognizing sequences as multiplication in disguise makes them much faster to work with.
Question 4 True / False
You can identify the rule of an arithmetic sequence by looking at just the first two terms.
TTrue
FFalse
Answer: False
Checking only the first two terms gives you a candidate rule, but not a confirmed one. Two numbers always have some difference — that doesn't mean the difference is constant throughout the sequence. A sequence like 2, 5, 9, 14... has a gap of 3 between the first two terms but the gaps keep increasing (not arithmetic at all). Always check at least three consecutive pairs before trusting the rule — a real arithmetic sequence has the same gap every time.
Question 5 Short Answer
How does identifying the common difference in an arithmetic sequence connect to multiplication? Why is that connection useful?
Think about your answer, then reveal below.
Model answer: The common difference tells you how much the sequence grows per step. Since every step adds the same amount, the total growth after n steps is n × (common difference) — multiplication. To find any term, multiply the number of steps taken by the common difference and add the starting value. This means you can calculate a distant term directly without listing every term in between.
This is one of the first glimpses of algebraic thinking in elementary math: the idea that you can find any value in a predictable pattern using a formula rather than counting up one step at a time. Patterns become powerful tools when you can jump to any point in them, not just march forward from the beginning.