Patterning - First Values from Equation for Geometric Pattern (Level 1)

This math topic involves determining the initial terms of geometric sequences by applying given algebraic expressions. It enhances the skills of recognizing patterns and performing exponentiation calculations with sequences starting from the first term (n=1). Students select the correct sequence generated by the equation from multiple choices. Each question features a different algebraic formula, testing a student's ability to calculate and understand geometric progressions where the common ratio and first term (initial term) are specified in the formulas.

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

First Values from Equation for Geometric Pattern

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Choose the first values that this equation would create starting with n=1

a_n = 1 \times 5^{n-1}

Patterning - First Values from Equation for Geometric Pattern Worksheet

Math worksheet on 'Patterning - First Values from Equation for Geometric Pattern (Level 1)'. Part of a broader unit on 'Patterns and Sums - Intro' Learn online: app.mobius.academy/math/units/patterns_and_sums_intro/

Choose the first values that this equation would create starting with n=1

A LaTex expression showing a sub n = 2 multiplied by 3 to the power of n-1

2, -1, -4, -7, -10, -13

2, 2, 2, 2, 2, 2

2, 6, 18, 54, 162, 486

-2, -6, -18, -54, -162, -486

2, 4, 8, 16, 32, 64

2, 8, 32, 128, 512, 2,048

Choose the first values that this equation would create starting with n=1

A LaTex expression showing a sub n = 1 multiplied by 2 to the power of n-1

1, 6, 36, 216, 1,296, 7,776

1, -2, 4, -8, 16, -32

1, -1, -3, -5, -7, -9

1, 2, 4, 8, 16, 32

0, 0, 0, 0, 0, 0

1, 3, 5, 7, 9, 11

Choose the first values that this equation would create starting with n=1

A LaTex expression showing a sub n = 1 multiplied by 5 to the power of n-1

-2, -10, -50, -250

Choose the first values that this equation would create starting with n=1

A LaTex expression showing a sub n = 3 multiplied by 3 to the power of n-1

3, 0, 0, 0, 0, 0

3, 9, 27, 81, 243, 729

3, 0, -3, -6, -9, -12

3, 18, 108, 648, 3,888, 23,328

3, 12, 48, 192, 768, 3,072

3, 6, 9, 12, 15, 18

Choose the first values that this equation would create starting with n=1

A LaTex expression showing a sub n = 3 multiplied by 2 to the power of n-1

3, 6, 12, 24, 48, 96

3, 1, -1, -3, -5, -7

3, 5, 7, 9, 11, 13

6, 12, 24, 48, 96, 192

3, 0, 0, 0, 0, 0

3, 5, 8, 13, 21, 34

Choose the first values that this equation would create starting with n=1

A LaTex expression showing a sub n = 2 multiplied by 4 to the power of n-1

-2, -8, -32, -128

Choose the first values that this equation would create starting with n=1

A LaTex expression showing a sub n = 3 multiplied by 4 to the power of n-1

7, 28, 112, 448