Find an equation for the nth term of the arithmetic sequence. -3, -5, -7, -9, ...

In an arithmetic sequence, the difference between any two consecutive terms is the same throughout the sequence.

Answer: The equation for the nth term of the arithmetic sequence -3, -5, -7, -9, ...... is -2n - 1.

Let's find the nth term of the sequence.

Explanation:

The equation for the nth term can be found using the formula \(a_{n}\) = [a + (n - 1) d]

In the sequence -3, -5, -7, -9, ......

Given, \(a_{1}\) = -3

d = \(a_{2}\) - \(a_{1}\) = -2

⇒ \(a_{n}\) = [a + (n - 1) d] 

⇒ \(a_{n}\) = [-3 + (n - 1) (-2)] 

⇒ \(a_{n}\) = [- 3 - 2n + 2]

⇒ \(a_{n}\) = -2n - 1

We can use an online arithmetic sequence calculator to calculate the nth term.

Thus, the equation for the nth term of the arithmetic sequence -3, -5, -7, -9, ...... is - 2n - 1.