Exploring Progressions in Mathematics

Define an arithmetic progression and provide an example.

• A collection of random numbers without any specific order. Example: 7, 2, 5, 9.

• An arithmetic progression is a sequence of numbers with a constant difference between consecutive terms. Example: 2, 5, 8, 11.

• A sequence of numbers with varying differences between terms. Example: 1, 3, 6, 10.

• A series of numbers that only includes even numbers. Example: 2, 4, 6, 8.

What is the common difference in the arithmetic sequence 3, 7, 11, 15?

• 4

• 2

• 8

• 6

Find the 10th term of the arithmetic progression where the first term is 5 and the common difference is 3.

• 28

• 32

• 35

• 25

If the first term of an arithmetic progression is 2 and the 5th term is 10, what is the common difference?

• 8

• 4

• 6

• 2

Write the formula for the nth term of an arithmetic progression.

• a_n = a_1 + (n - 1)d

• a_n = a_1 * n + d

• a_n = n^2 + d

• a_n = a_1 - (n + 1)d

What is the sum of the first 20 terms of the arithmetic progression 4, 8, 12, ...?

• 840

• 800

• 600

• 1000

Define a geometric progression and provide an example.

• 5, 10, 15, 20

• 3, 9, 27, 81

• 1, 2, 3, 4

• An example of a geometric progression is 2, 6, 18, 54.

What is the common ratio in the geometric sequence 2, 6, 18, 54?

• 6

• 2

• 3

• 4

Find the 6th term of the geometric progression where the first term is 3 and the common ratio is 2.

• 72

• 64

• 96

• 48

If the first term of a geometric progression is 5 and the 4th term is 80, what is the common ratio?

• 15

• 2

• 3

• 10