Finding the Nth Term of a Geometric Sequence

To find the next term in a geometric sequence …

• add the common difference d

• multiply by the common ratio r

• subtract the common difference d

• divide by the common ratio r

Answer explanation

In a geometric sequence, each term is found by multiplying the previous term by the common ratio r. Therefore, to find the next term, you multiply by the common ratio r.

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CCSS.HSF.BF.A.2

• common difference

• nth term

• common ratio

• first term

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CCSS.HSF.BF.A.2

Solving for the nth term of geometric sequence, given that a₁ = 4 and r= 6, what is the value of the 4th term?

• 144

• 864

• 124

• 764

Answer explanation

To find the 4th term of a geometric sequence, use the formula a_n = a_1 * r^(n-1). Here, a_1 = 4, r = 6, and n = 4. Thus, a_4 = 4 * 6^(4-1) = 4 * 216 = 864. Therefore, the 4th term is 864.

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CCSS.HSF.BF.A.2

Find the 10th term of the following geometric sequence

5, 20, 80, 320, ...

• 81,920

• 327,680

• 1,310,720

• 5,242,880

Answer explanation

The sequence is geometric with a common ratio of 4. The nth term is given by a_n = a_1 * r^(n-1). Here, a_1 = 5, r = 4, and n = 10. Thus, a_{10} = 5 * 4^9 = 1,310,720, which is the correct answer.

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CCSS.HSF.BF.A.2

Please click on the picture and read carefully

• a

• b

• c

• d

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CCSS.HSF.BF.A.2

What is the 11th term of the geometric sequence?

• -5120

• 97,656,250

• 19,531,250

• -19,531,250

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CCSS.HSF.BF.A.2

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CCSS.HSF.BF.A.2

• A

• B

• C

• D

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CCSS.HSF.BF.A.2

Values of the terms of a geometric sequence are graphed in the figure above.  Which of the following is an expression for the nth term of the geometric sequence?

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CCSS.HSF-IF.C.8B

In the sequence of numbers, g₃ = -27, g₄ = -81, g₅ = -243, g₆ = -729, and g₇ = -2187. Based on this information, which equation can be used to find the nth term in the sequence, g_n?

• g_n = -27 ∙ 3ⁿ⁺¹

• g_n = -27 ∙ 3^n-1

• g_n = -3 ∙ 3ⁿ⁺¹

• g_n = -3 ∙ 3^n-1

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CCSS.HSF.BF.A.2