Recursive and Explicit formulas
Authored by Eric Fonjah
Mathematics
9th - 10th Grade
CCSS covered
Used 387+ times
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About
This quiz focuses on arithmetic and geometric sequences, covering both recursive and explicit formulas at the high school level, specifically grades 9-10. Students need to understand the fundamental difference between arithmetic sequences (where consecutive terms have a constant difference) and geometric sequences (where consecutive terms have a constant ratio). The core concepts include identifying common differences and common ratios, writing explicit formulas in the form a_n = a_1 + d(n-1) for arithmetic sequences and a_n = a_1(r)^(n-1) for geometric sequences, and converting between recursive and explicit representations. Students must demonstrate fluency in pattern recognition, algebraic manipulation, and the ability to find specific terms using formulas or by extending patterns manually. Created by Eric Fonjah, a Mathematics teacher in the US who teaches grades 9-10. This comprehensive assessment serves multiple instructional purposes, from introducing sequence concepts during direct instruction to providing formative feedback on student understanding of algebraic representations. Teachers can use this quiz as a warm-up to activate prior knowledge about patterns, as guided practice during lessons on sequence notation, or as homework to reinforce the connection between recursive and explicit formulas. The varied question types make it excellent for differentiated review sessions and identifying specific areas where students need additional support with sequence manipulation. This assessment aligns with Common Core standards A-SSE.A.1 and F-BF.A.2, which focus on interpreting expressions and writing arithmetic sequences both recursively and with explicit formulas.
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20 questions
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1.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence.
an = 4n + 29
an = 25 +(-4)(n-1)
an = -25 +(-4)(n-1)
an = 4n + 25
Tags
CCSS.HSF.BF.A.2
2.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
The next two terms of the sequence 4,7,10,13 are
Tags
CCSS.HSF.BF.A.2
3.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Write the explicit formula for the sequence -4, -6, -8, -10,...
an = -4 + (-2)(n-1)
an = 4 + (-2)(n-1)
an = -4 - 2(n-1)
an = -4 + 2(n-1)
Tags
CCSS.HSF.BF.A.2
4.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
What is the common ratio for the sequence:
3, 15, 75...
12
1/5
5
4
Tags
CCSS.HSF.BF.A.2
5.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
What is the explicit rule for the sequence:
11, 22, 44, 88...
an = 2(11)n-1
an = 11x2
an = 11(2)n-1
a1 = 11 ; an+1 = an * 2
Tags
CCSS.HSF.LE.A.2
6.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
Identify the common difference.
10, 20, 30, 40, ...
5
10
15
20
Tags
CCSS.HSF.BF.A.2
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What is a1?
3, 15, 75, 375, 1875...
Tags
CCSS.HSF.BF.A.2
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