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Patterning

Equation for Decreasing Arithmetic Pattern (Level 1)

This math topic focuses on recognizing and formulating equations for decreasing arithmetic patterns. Across several problems, students are presented with sequences of numbers and are tasked with selecting the correct equation that describes the pattern where \(n=1\) is the first term. Options for the equations are provided in various formats, and students must identify the accurate arithmetic expression that continues the sequence logically. The skill level is designed for advanced pattern recognition and algebraic thinking. This topic is part of a broader unit on "Patterns and Sums - Advanced".

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

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Patterning - Equation for Decreasing Arithmetic Pattern Worksheet

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Patterning - Equation for Decreasing Arithmetic Pattern
1
Find the correct equation to describe this decreasing pattern where n=1 is the first term
23, 18, 13, 8
a A LaTex expression showing a sub n = 23 - 8(n-1)
b A LaTex expression showing a sub n = 23 - 5(n-1)
c A LaTex expression showing a sub n = 23 + 5(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 = 23 multiplied by 5 to the power of n-1
f A LaTex expression showing a sub n = 23 - 5(n)
2
Find the correct equation to describe this decreasing pattern where n=1 is the first term
13, 10, 7, 4
a A LaTex expression showing a sub n = a sub n-2 + a sub n-1
b A LaTex expression showing a sub n = 13 - 1(n-1)
c A LaTex expression showing a sub n = 13 + 3(n-1)
d A LaTex expression showing a sub n = 13 - 3(n-1)
e A LaTex expression showing a sub n = 13 - 3(n)
f A LaTex expression showing a sub n = 13 - 0(n-1)
3
Find the correct equation to describe this decreasing pattern where n=1 is the first term
28, 23, 18, 13, 8
a A LaTex expression showing a sub n = 28 - 5(n-1)
b A LaTex expression showing a sub n = 26 - 5(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 = 28 - 5(n)
e A LaTex expression showing a sub n = 28 - 8(n-1)
f A LaTex expression showing a sub n = 28 - 2(n-1)
4
Find the correct equation to describe this decreasing pattern where n=1 is the first term
11, 9, 7, 5
a A LaTex expression showing a sub n = 11 - 2(n-1)
b A LaTex expression showing a sub n = 11 - 3(n-1)
c A LaTex expression showing a sub n = 11 + 2(n-1)
d A LaTex expression showing a sub n = 11 - 1(n-1)
e A LaTex expression showing a sub n = 11 - 2(n)
f A LaTex expression showing a sub n = 11 - 0(n-1)
5
Find the correct equation to describe this decreasing pattern where n=1 is the first term
16, 13, 10, 7, 4
a A LaTex expression showing a sub n = 16 - 3(n)
b A LaTex expression showing a sub n = 16 + 3(n-1)
c A LaTex expression showing a sub n = 16 - 3(n-1)
d A LaTex expression showing a sub n = 16 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 = 16 - 4(n-1)
6
Find the correct equation to describe this decreasing pattern where n=1 is the first term
27, 21, 15, 9
a A LaTex expression showing a sub n = 27 - 6(n)
b A LaTex expression showing a sub n = 28 - 6(n-1)
c A LaTex expression showing a sub n = 27 multiplied by 6 to the power of n-1
d A LaTex expression showing a sub n = 27 - 6(n-1)
e A LaTex expression showing a sub n = 27 + 6(n-1)
f A LaTex expression showing a sub n = 27 - 7(n-1)
7
Find the correct equation to describe this decreasing pattern where n=1 is the first term
32, 26, 20, 14, 8
a A LaTex expression showing a sub n = 32 - 6(n-1)
b A LaTex expression showing a sub n = a sub n-2 + a sub n-1
c A LaTex expression showing a sub n = 32 multiplied by 6 to the power of n-1
d A LaTex expression showing a sub n = 32 - 6(n)
e A LaTex expression showing a sub n = 32 - 9(n-1)
f A LaTex expression showing a sub n = 29 - 6(n-1)
8
Find the correct equation to describe this decreasing pattern where n=1 is the first term
11, 9, 7, 5, 3
a A LaTex expression showing a sub n = 9 - 2(n-1)
b A LaTex expression showing a sub n = 11 - -2(n-1)
c A LaTex expression showing a sub n = 11 multiplied by 2 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 = 11 - 2(n)
f A LaTex expression showing a sub n = 11 - 2(n-1)