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Patterning - Equation from Rule for Geometric Pattern (Level 1)

This math topic involves generating the equations of geometric sequences from given rules for each pattern. The students are provided a rule (such as "start at a number and multiply by a specific number for each subsequent term"), and they need to derive the equation describing this sequence. Each question offers multiple choices represented in LaTeX format, and students must identify the correct mathematical representation that matches the described pattern, testing their understanding of geometric sequences and equation formation.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Equation from Rule for Geometric Pattern

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Find the correct equation that this pattern rule describes

Start at 2 and multiply by 2 for each term

Patterning - Equation from Rule for Geometric Pattern Worksheet

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Math worksheet on 'Patterning - Equation from Rule for Geometric Pattern (Level 1)'. Part of a broader unit on 'Patterns and Sums - Practice' Learn online: app.mobius.academy/math/units/patterns_and_sums_practice/
1
Start at 2 and multiply by 5 for each term
Find the correct equation that this pattern rule describes
a A LaTex expression showing a sub n = 2 multiplied by 5 to the power of n-1
b A LaTex expression showing a sub n = 5 multiplied by 5 to the power of n-1
c A LaTex expression showing a sub n = 2 multiplied by 8 to the power of n-1
d A LaTex expression showing a sub n = 2 multiplied by 5 to the power of n
e A LaTex expression showing a sub n = 2 multiplied by 1 to the power of n-1
f A LaTex expression showing a sub n = 2 multiplied by 4 to the power of n-1
2
Start at 2 and multiply by 3 for each term
Find the correct equation that this pattern rule describes
a A LaTex expression showing a sub n = 2 multiplied by 3 to the power of n
b A LaTex expression showing a sub n = 5 multiplied by 3 to the power of n-1
c A LaTex expression showing a sub n = a sub n-2 + a sub n-1
d A LaTex expression showing a sub n = 2 multiplied by 3 to the power of n-1
e A LaTex expression showing a sub n = 2 + 3(n-1)
f A LaTex expression showing a sub n = 2 - 3(n-1)
3
Start at 3 and multiply by 5 for each term
Find the correct equation that this pattern rule describes
a A LaTex expression showing a sub n = 3 multiplied by 5 to the power of n-1
b A LaTex expression showing a sub n = -1 multiplied by 5 to the power of n-1
c A LaTex expression showing a sub n = 3 + 5(n-1)
d A LaTex expression showing a sub n = 3 multiplied by 5 to the power of n
e A LaTex expression showing a sub n = 1 multiplied by 5 to the power of n-1
f A LaTex expression showing a sub n = a sub n-2 + a sub n-1
4
Start at 1 and multiply by 5 for each term
Find the correct equation that this pattern rule describes
a A LaTex expression showing a sub n = 3 multiplied by 5 to the power of n-1
b A LaTex expression showing a sub n = -3 multiplied by 5 to the power of n-1
c A LaTex expression showing a sub n = 1 multiplied by 5 to the power of n-1
d A LaTex expression showing a sub n = a sub n-2 + a sub n-1
e A LaTex expression showing a sub n = 1 multiplied by 5 to the power of n
f A LaTex expression showing a sub n = 1 - 5(n-1)
5
Start at 3 and multiply by 4 for each term
Find the correct equation that this pattern rule describes
a A LaTex expression showing a sub n = 3 multiplied by 3 to the power of n-1
b A LaTex expression showing a sub n = 3 multiplied by 4 to the power of n
c A LaTex expression showing a sub n = a sub n-2 + a sub n-1
d A LaTex expression showing a sub n = 3 + 4(n-1)
e A LaTex expression showing a sub n = 3 multiplied by 2 to the power of n-1
f A LaTex expression showing a sub n = 3 multiplied by 4 to the power of n-1
6
Start at 3 and multiply by 2 for each term
Find the correct equation that this pattern rule describes
a A LaTex expression showing a sub n = 7 multiplied by 2 to the power of n-1
b A LaTex expression showing a sub n = -1 multiplied by 2 to the power of n-1
c A LaTex expression showing a sub n = 3 + 2(n-1)
d A LaTex expression showing a sub n = a sub n-2 + a sub n-1
e A LaTex expression showing a sub n = 3 multiplied by 2 to the power of n-1
f A LaTex expression showing a sub n = 3 multiplied by 2 to the power of n
7
Start at 1 and multiply by 2 for each term
Find the correct equation that this pattern rule describes
a A LaTex expression showing a sub n = 1 - 2(n-1)
b A LaTex expression showing a sub n = 1 multiplied by -1 to the power of n-1
c A LaTex expression showing a sub n = 1 multiplied by 1 to the power of n-1
d A LaTex expression showing a sub n = 1 multiplied by 2 to the power of n
e A LaTex expression showing a sub n = 1 multiplied by 2 to the power of n-1
f A LaTex expression showing a sub n = -3 multiplied by 2 to the power of n-1