Grade 11 · Algebra & functions

Geometric sequence equations practice

Geometric sequence equations is a grade 11 math skill aligned to Common Core standard HSF.BF.A.2: write arithmetic and geometric sequences both recursively and with an explicit formula, and use them to model situations. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 geometric sequence equations problems our math games drill.

CCSS HSF.BF.A.210 questions in the bank
Sample questions

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Question 1easy

The first term of a sequence is 55. Each term after the first is 33 times the preceding term. If ww represents the nnth term of the sequence, which equation gives ww in terms of nn?

The first term is 55 and each step multiplies by 33, so after n−1n - 1 multiplications the nnth term is w=5⋅3n−1w = 5 \cdot 3^{n-1}.

Question 2easy

The first term of a sequence is 22. Each term after the first is 44 times the preceding term. If ana_n represents the nnth term, which equation gives ana_n in terms of nn?

With a1=2a_1 = 2 and common ratio 44, the nnth term is an=2⋅4n−1a_n = 2 \cdot 4^{n-1}.

Question 3easy

The first term of a sequence is 88. Each term after the first is 22 times the preceding term. If f(n)f(n) represents the nnth term, which equation gives f(n)f(n) in terms of nn?

Starting at 88 and doubling each step gives f(n)=8⋅2n−1f(n) = 8 \cdot 2^{n-1}.

Question 4easy

The first term of a sequence is 66. Each term after the first is 33 times the preceding term. If ww represents the nnth term, which equation gives ww in terms of nn?

Multiplying by 33 a total of n−1n - 1 times after the initial 66 gives w=6⋅3n−1w = 6 \cdot 3^{n-1}.

Question 5easy

The first term of a sequence is 1010. Each term after the first is 22 times the preceding term. If ana_n represents the nnth term, which equation gives ana_n in terms of nn?

A geometric sequence with a1=10a_1 = 10 and r=2r = 2 has an=10⋅2n−1a_n = 10 \cdot 2^{n-1}.

Question 6easy

The first term of a sequence is 44. Each term after the first is 55 times the preceding term. If f(n)f(n) represents the nnth term, which equation gives f(n)f(n) in terms of nn?

Each of the n−1n - 1 gaps between the first and nnth terms contributes a factor of 55, so f(n)=4⋅5n−1f(n) = 4 \cdot 5^{n-1}.

Question 7easy

The first term of a sequence is 77. Each term after the first is 22 times the preceding term. If ww represents the nnth term, which equation gives ww in terms of nn?

Doubling from a start of 77 gives w=7⋅2n−1w = 7 \cdot 2^{n-1}.

Question 8easy

The first term of a sequence is 99. Each term after the first is 33 times the preceding term. If ana_n represents the nnth term, which equation gives ana_n in terms of nn?

With a1=9a_1 = 9 and common ratio 33, the explicit form is an=9⋅3n−1a_n = 9 \cdot 3^{n-1}.

Tests that cover geometric sequence equations:
SBACSATACTNY State MathNC EOG/EOC
More Grade 11 skills:
Function transformationsLogarithm rulesExponential and log formulasSequences and seriesComplex number operationsBinomial theorem and factorialsConic sectionsAll Grade 11 practice →

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