AI Tutor
Imagine you are stacking toy blocks into towers of 2, 5, 8, and 11. An additive pattern is a list of numbers that grows by adding the exact same amount each time.
How can you figure out the secret rule when numbers are missing at the end?

Continuing the Pattern

To find the rule of an increasing pattern, calculate the difference between two consecutive terms: Rule=Next Term−Current Term\text{Rule} = \text{Next Term} - \text{Current Term} (for example, 10−4=610 - 4 = 6).
To continue the pattern, repeatedly add the constant step: Next Term=Previous Term+Constant Step\text{Next Term} = \text{Previous Term} + \text{Constant Step}. Adding 66 gives 22+6=2822 + 6 = 28 and 28+6=3428 + 6 = 34.
Always check at least two pairs of neighbors (like 10−4=610 - 4 = 6 and 16−10=616 - 10 = 6) to prove the jump stays the same!

Key takeaways

  • An additive increasing pattern is a sequence of numbers (or objects) that grows larger by adding the same constant amount each time (e.g., +2+2, +3+3, +5+5, +10+10).
  • To find the rule of an increasing pattern, determine the difference between two consecutive terms: Rule=Next Term−Current Term\text{Rule} = \text{Next Term} - \text{Current Term}.
  • Check multiple consecutive terms in the sequence to ensure the pattern increases by a constant amount (e.g., in 4,7,10,134, 7, 10, 13, the step from 4→74 \to 7 is +3+3, 7→107 \to 10 is +3+3, and 10→1310 \to 13 is +3+3).
  • To continue an increasing pattern, repeatedly apply the constant addition rule to the last known term: Next Term=Previous Term+Constant Step\text{Next Term} = \text{Previous Term} + \text{Constant Step}.