Question

The first five terms of an arithmetic sequence are shown below:

20, 17, 14, 11, 8, . . .
Let n represent the term number and f(n) the term in the sequence.
Choose a function that represents the sequence.

The answer to this question is f(n) = -3 + 23

Now my question is, how do you find the solution? I was taught the explicit formula is f(n) = m(n) + b, but no matter how many times I've tried to plug in the numbers I cannot seem to get the right answer. Please help me and do show the entire process and the steps.

Answer 1

Y'all know what it is already, but I want points, so: f(n) = -3n + 23

Answer 2

The function represents the sequence is - 3 n + 23.

Explanation:

20. 17, 14, 11, 8,......

Here, the first term is

a = 20

Common difference, d = -3

Let the nth term is Tn.

Tn = a + (n -1) d

Tn = 20 + (n -1) x (-3)

Tn = 20 - 3 n + 3

Tn = 23 - 3 n = - 3 n + 23

So, the function represents the sequence is - 3 n + 23.