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Patterning

Equation for Geometric Pattern (Level 1)

This math topic focuses on identifying the correct equations to describe various geometric patterns. Each question presents a sequence of numbers and asks to select the equation that generates this sequence where \( n = 1 \) is the first term of the sequence. The sequences include simple numerical progressions with geometric growth, requiring the understanding of how to represent such patterns using algebraic equations featuring exponents or factors. The skill practiced is recognizing and formulating geometric sequences and the equations that represent each given pattern.

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

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Patterning - Equation for Geometric Pattern Worksheet

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Patterning - Equation for Geometric Pattern
1
2, 4, 8, 16, 32, 64
Find the correct equation to describe this geometric pattern where n=1 is the first term
a A LaTex expression showing a sub n = 2 multiplied by 2 to the power of n
b A LaTex expression showing a sub n = 2 multiplied by 2 to the power of n-1
c A LaTex expression showing a sub n = 2 + 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 = 2 multiplied by -2 to the power of n-1
f A LaTex expression showing a sub n = 2 - 2(n-1)
2
1, 3, 9, 27, 81, 243
Find the correct equation to describe this geometric pattern where n=1 is the first term
a A LaTex expression showing a sub n = 1 + 3(n-1)
b A LaTex expression showing a sub n = 1 multiplied by 3 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 = 1 multiplied by 3 to the power of n-1
e A LaTex expression showing a sub n = -2 multiplied by 3 to the power of n-1
f A LaTex expression showing a sub n = 5 multiplied by 3 to the power of n-1
3
Find the correct equation to describe this geometric pattern where n=1 is the first term
1, 2, 4, 8, 16, 32
a A LaTex expression showing a sub n = 1 multiplied by 2 to the power of n-1
b A LaTex expression showing a sub n = 1 multiplied by 6 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 = 1 - 2(n-1)
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 = 1 multiplied by 2 to the power of n
4
Find the correct equation to describe this geometric pattern where n=1 is the first term
3, 15, 75, 375
a A LaTex expression showing a sub n = 3 - 5(n-1)
b A LaTex expression showing a sub n = 2 multiplied by 5 to the power of n-1
c A LaTex expression showing a sub n = 3 multiplied by 5 to the power of 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 = 3 multiplied by 6 to the power of n-1
f A LaTex expression showing a sub n = 5 multiplied by 5 to the power of n-1
5
3, 9, 27, 81, 243, 729
Find the correct equation to describe this geometric pattern where n=1 is the first term
a A LaTex expression showing a sub n = 3 multiplied by 3 to the power of n
b A LaTex expression showing a sub n = 3 multiplied by 0 to the power of n-1
c A LaTex expression showing a sub n = 3 multiplied by -1 to the power of n-1
d A LaTex expression showing a sub n = 3 multiplied by 3 to the power of n-1
e A LaTex expression showing a sub n = a sub n-2 + a sub n-1
f A LaTex expression showing a sub n = 6 multiplied by 3 to the power of n-1
6
Find the correct equation to describe this geometric pattern where n=1 is the first term
1, 5, 25, 125
a A LaTex expression showing a sub n = a sub n-2 + a sub 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 multiplied by 5 to the power of n-1
d A LaTex expression showing a sub n = 1 + 5(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)
7
Find the correct equation to describe this geometric pattern where n=1 is the first term
3, 12, 48, 192
a A LaTex expression showing a sub n = 3 - 4(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 = 3 multiplied by 1 to the power of n-1
d A LaTex expression showing a sub n = 6 multiplied by 4 to the power of n-1
e A LaTex expression showing a sub n = 3 multiplied by 4 to the power of n-1
f A LaTex expression showing a sub n = a sub n-2 + a sub n-1
8
3, 6, 12, 24, 48, 96
Find the correct equation to describe this geometric pattern where n=1 is the first term
a A LaTex expression showing a sub n = 3 multiplied by -2 to the power of n-1
b A LaTex expression showing a sub n = 2 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 = -1 multiplied by 2 to the power of n-1