Question

What is the nth term rule of the linear sequence below?
27, 25, 23, 21, 19, …

Answer 1

`a_n = 27 -2(n-1)\\\\`

Explanation:

This is an arithmetic sequence

The common difference (the difference between any two terms is -2)

The nth term of an arithmetic sequence is given by the expression

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

`\text{$a_1$ is the first term } =27\\\text{n is the term number}\\\text{d is the common difference} = -2\\`

So, for this particular sequence

`a_n = 27 -2(n-1)\\\\`

Check:

`a_1 = 27 -2(1-1) = 27 - 0 = 27\\\\a_2 = 27-2(2-1) = 27-2 = 25\\\\\\a_5=27-2(5-1) = 27 - 2(4) = 27 - 8 = 19`