The video tutorial covers the basics of geometric sequences, explaining the difference between arithmetic and geometric sequences. It introduces the formula for finding the nth term in a geometric sequence and provides examples of calculating specific terms, such as the 23rd, 8th, and 25th terms. The tutorial also explores more advanced applications, including finding the first term given a term and common ratio, and solving for terms using substitution.

What is the main difference between an arithmetic sequence and a geometric sequence?

• Both sequences involve multiplication.

• Both sequences involve addition.

• Arithmetic sequences involve addition, while geometric sequences involve multiplication.

• Arithmetic sequences involve multiplication, while geometric sequences involve addition.

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CCSS.HSF.BF.A.2

In a geometric sequence, what does the 'r' represent in the formula a_n = a_1 * r^(n-1)?

• The nth term

• The common ratio

• The common difference

• The first term of the sequence

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CCSS.HSF.BF.A.2

If the first term of a geometric sequence is 13 and the common ratio is 2, what is the 23rd term?

• 54525952

• 1048576

• 8388608

• 4194304

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CCSS.HSF.BF.A.2

Given a geometric sequence with a first term of 1 and a common ratio of 5, what is the 8th term?

• 3125

• 15625

• 78125

• 625

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CCSS.HSF.BF.A.2

In a geometric sequence, if the first term is 4 and the common ratio is 2.5, what is the 25th term?

• 1421854.72

• 14218547.2

• 142185.472

• 142185472

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CCSS.HSF.BF.A.2

If you are given a term in a geometric sequence and the common ratio, what can you find?

• Only the nth term

• Only the common ratio

• Only the first term

• Both the first term and any other term

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CCSS.HSF.BF.A.2

Given a geometric sequence where A3 = -36 and the common ratio is 6, what is the first term?

• -36

• 36

• -1

• 1

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CCSS.HSF.BF.A.2

In a geometric sequence, if A5 = 324 and A3 = 36, what is the common ratio?

• 3

• 2

• 6

• 9

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CCSS.HSF.BF.A.2

If the common ratio in a geometric sequence is 3 and the first term is 4, what is the 12th term?

• 14348907

• 4782969

• 1594323

• 531441

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CCSS.HSF.BF.A.2

When given two terms in a geometric sequence, what is the first step to find the common ratio?

• Multiply the terms

• Divide the terms

• Add the terms

• Subtract the terms

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CCSS.HSF.BF.A.2