Complete a geometric number pattern

Learning Objectives Define what a geometric number pattern is. Identify the multiplicative or divisive rule in a given geometric pattern. Use the identified rule to find missing terms in a geometric pattern. Distinguish between arithmetic and geometric patterns. Apply geometric patterns to solve simple real-world problems. Explain their reasoning for identifying a pattern rule. Have you ever noticed how some things grow or shrink by multiplying? 📈 Like a snowball rolling down a hill, getting bigger and bigger! What if numbers did that too? In this lesson, we'll explore 'geometric number patterns,' where numbers change by multiplying or dividing by the same amount each time. Understanding these patterns helps us predict what comes next and see how things grow...

TermDefinitionExample PatternA sequence of numbers, shapes, or objects that repeats or follows a rule.2, 4, 6, 8, ... (a pattern of adding 2) Geometric PatternA number pattern where each term after the first is found by multiplying or dividing the previous term by a fixed, non-zero number.3, 6, 12, 24, ... (each number is multiplied by 2) TermEach individual number in a sequence or pattern.In the pattern 2, 4, 8, 16, the number '8' is the third term. Rule (Pattern Rule)The operation (multiplication or division) and the number that consistently changes one term into the next in a geometric pattern.For 5, 10, 20, 40, the rule is 'multiply by 2'. MultiplierThe number by which you multiply each term to get the next term in a geometric pattern.In 4, 12, 36, the multiplier i...

Identifying the Multiplicative Rule $T_n = T_{n-1} \times R$ To find the rule, divide any term by its preceding term. If the result (R) is the same for all pairs, then R is your multiplier. $T_n$ is the current term, $T_{n-1}$ is the previous term. Identifying the Divisive Rule $T_n = T_{n-1} \div R$ To find the rule, divide any term by its preceding term. If the result (R) is a fraction or decimal less than 1, or if the pattern is decreasing, you might be dividing. Alternatively, you can find what number (R) you divide by to get the next term. $T_n$ is the current term, $T_{n-1}$ is the previous term. Completing the Pattern Next Term = Current Term $\times$ Rule (or $\div$ Rule) Once the rule is identified, apply it repeatedly to the last known term to find the subs...