Exploring Sequences in Mathematics

What is the 10th term of the arithmetic sequence 3, 7, 11, ...?

• 45

• 35

• 30

• 39

If the first term of a geometric sequence is 5 and the common ratio is 2, what is the 6th term?

• 80

• 320

• 40

• 160

Determine the sum of the first 20 terms of the arithmetic sequence 4, 8, 12, ...

• 840

• 600

• 1000

• 800

Find the common difference of the arithmetic sequence 15, 10, 5, ...

• 5

• -5

• -10

• 0

What is the formula for the nth term of a geometric sequence?

• a_n = r^(n-1)

• a_n = a_1 * n * r

• a_n = a_1 * r^(n-1)

• a_n = a_1 + r^(n-1)

If the 5th term of an arithmetic sequence is 20 and the common difference is 3, what is the first term?

• 8

• 15

• 12

• 5

Calculate the sum of the first 10 terms of the geometric sequence 1, 3, 9, ...

• 29524

• 512

• 100

• 27

What is the 7th term of the arithmetic sequence defined by the formula a_n = 2n + 1?

• 25

• 10

• 20

• 15

If the first term of a geometric sequence is 10 and the common ratio is 0.5, what is the 4th term?

• 1.25

• 2.5

• 5

• 0.625

How do you determine if a sequence is arithmetic or geometric?

• A sequence is arithmetic if the terms are in increasing order; it is geometric if the terms are all positive.

• A sequence is arithmetic if the first term is greater than the last term; it is geometric if the last term is a multiple of the first term.

• A sequence is arithmetic if the differences between terms are constant; it is geometric if the ratios of consecutive terms are constant.

• A sequence is arithmetic if the sum of the terms is constant; it is geometric if the product of the terms is constant.