Finding the nth Term of a Geometric Sequence

What do we call the individual numbers in a sequence?

• Common difference

• Common ratio

• First Term

• Term

Answer explanation

In a sequence, the individual numbers are referred to as 'terms'. Each term represents a specific position in the sequence, distinguishing it from concepts like common difference or common ratio.

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.

• common difference

• nth term

• common ratio

• first term

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.

What is the 5th term of the sequence 7, 14, 28, ...?

• 72

• 48

• 56

• 112

Answer explanation

The sequence doubles each term: 7, 14 (7x2), 28 (14x2). Continuing this pattern, the 4th term is 56 (28x2) and the 5th term is 112 (56x2). Thus, the 5th term is 112.

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.

Find the 10th term of the following geometric sequence

- 7, 7, - 7, ...

• - 7

• 7

• - 1

• 1

Answer explanation

The sequence alternates between -7 and 7. The 1st term is -7, the 2nd is 7, the 3rd is -7, and so on. The 10th term, being even, follows the pattern and is 7.

Find the 11th term of the following geometric sequence

- 7, 7, - 7, ...

• - 7

• 7

• - 1

• 1

Answer explanation

The sequence alternates between -7 and 7. The 11th term is the same as the 1st term, which is -7. Therefore, the correct answer is -7.

Find the 12th term of the following geometric sequence

7, - 7, - 7, ...

• - 7

• 7

• - 1

• 1

Answer explanation

The sequence alternates between 7 and -7. Since the 1st term is 7 and the 2nd term is -7, the 12th term, being even, will also be -7. Thus, the correct answer is -7.

What is the 12th term of a geometric sequence if a₆ = - 96 and a₉ = 768?

• - 12,288

• - 6,144

• 6,144

• 12,288

Answer explanation

In a geometric sequence, the ratio between terms is constant. Given a6 = -96 and a9 = 768, we find the common ratio and use it to calculate a12. The 12th term a12 = a9 * r^3 = 768 * (-2) = -6144.