Question

Write an equation for the nth term of the arithmetic sequence –1, –3, –5, –7,

Answer 1

`a_(n)` = 1 - 2n

Explanation:

The nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = a₂ - a₁ = - 3 - (- 1) = - 3 + 1 = - 2 , then

`a_(n)` = - 1 - 2(n - 1) = - 1 - 2n + 2 = - 2n + 1 = 1 - 2n

Answer 2

`a_n=-1+(n-1)(-2)`

Explanation:

The arithmetic sequence formula looks like this:

`a_n=a_1+(n-1)d`

where aₙ is the nth term, a₁ is the first term, n is the index, and d is the common difference.

Each consecutive term is decreased by 2 over the last, so d = 2. The first term is -1 of course, so you can write this equation:

`a_n=-1+(n-1)(-2)`

Just to confirm:

`a_n=-1+(n-1)(-2)\\a_3=-1+(2)(-2)\\a_3=-1-4\\a_3=-5`

And it works, -5 is the 3rd term in the sequence.