Arithmetic Sequences Quiz

What is the common difference and the first term in the arithmetic sequence 2, 5, 8, 11?

What are the next three terms in the sequence 2, 5, 8, 11?

Calculate u0, u1, and u2 for the sequence defined by un = 2 - 3n.

How can you prove that the sequence (un)n∈ℕ defined by un = 2 - 3n is arithmetic?

Is the sequence (wp)p∈ℕ defined by wp = (p+1)² arithmetic, and what are w0, w1, and w2?

Arithmetic Sequences

An arithmetic sequence is a sequence where the difference between consecutive terms is constant.
This constant difference is called the common difference.
If the common difference (r) is 0, all terms in the sequence are equal to the first term.
To find the next term in an arithmetic sequence, add the common difference to the current term.

Example Arithmetic Sequence

The sequence 2, 5, 8, 11,... is arithmetic.
The common difference (r) is 3.
The first term is 2.
Three more terms in the sequence are 14, 17, and 20.

Sequence Defined by Formula

The sequence (un) where un = 2 - 3n is arithmetic.
u0 = 2, u1 = -1, and u2 = -4.
To prove the sequence is arithmetic, show that the difference between any two consecutive terms is constant:
- un+1 - un = (2 - 3(n+1)) - (2 - 3n) = -3, which is constant.

Non-Arithmetic Sequence

The sequence (wp) where wp = (p+1)^2 is not arithmetic.
w0 = 1, w1 = 4, and w2 = 9.
The difference between consecutive terms is not constant:
- w1 - w0 = 3
- w2 - w1 = 5

Test your understanding of arithmetic sequences with this quiz. Explore key concepts such as common differences and sequence definitions through example problems. Determine whether given sequences are arithmetic or not.