What does $$a_1$$ represent in the formula $$a_n = a_1 r^{(n-1)}$$ ?

$$a_1$$ represents the first term of the geometric sequence.

If $$a_n = -4(2)^{(n-1)}$$ , what is $$a_8$$ ?

$$a_8 = -4(2)^{(8-1)} = -4(2^7) = -4(128) = -512$$ .

What is the formula to find the sum of the first n terms of a geometric sequence?

The sum of the first n terms of a geometric sequence is given by: $$S_n = a_1 \times \frac{1 - r^n}{1 - r}$$ , for @@r eq 1@@.

What is the value of $$a_8$$ if $$a_n = 4(4)^{(n-1)}$$ ?

$$a_8 = 4(4)^{(8-1)} = 4(4^7) = 4(16384) = 65536$$ .

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

In a geometric sequence, each term is multiplied by a constant (common ratio), while in an arithmetic sequence, each term is added to a constant (common difference).

How can you identify a geometric sequence from a list of numbers?

A sequence is geometric if the ratio of consecutive terms is constant.

What is the first term of the sequence defined by $$a_n = 10(2)^{(n-1)}$$ ?

The first term is $$a_1 = 10(2)^{(1-1)} = 10(2)^0 = 10$$ .

If the common ratio is 1, what type of sequence is it?

If the common ratio is 1, the sequence is a constant sequence, where all terms are the same.

Geometric Sequences Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

2.

FLASHCARD QUESTION

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

3.

FLASHCARD QUESTION

Front

What is the recursive formula for a geometric sequence?

Back

4.

FLASHCARD QUESTION

Front

What is the explicit formula for a geometric sequence?

Back

5.

FLASHCARD QUESTION

Front

Given the sequence 3, 6, 12, 24, what is the common ratio?

Back

The common ratio is 2, since each term is multiplied by 2 to get the next term.

6.

FLASHCARD QUESTION

Front

How do you find the nth term of a geometric sequence?

Back

7.

FLASHCARD QUESTION

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?

Back

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