Question

How do you find the explicit formula for the following sequence 20,15,10,5,0?

Answer 1

To find the explicit formula for an arithmetic sequence you must use the formula `t_n = a+ (n - 1)d`.

Explanation:

In the formula given above:

-`t_n` is the nth term

-`n` is the term's number in the sequence.

-`d` is the common difference separating the terms in your sequence

-`a` is the first term

`t_n = 20 + (n - 1)xx -5`

`t_n = 20 - 5n + 5`

`t_n = 25 - 5n`

This formula is now completely simplified, and as soon as you plug in a number for `n`, or a term, you can find it's term or it's number in the sequence, respectively.

Example

Find the 26th term in the sequence.

`t_26 = 25 - 5 xx 26`

`t_26 = 25 - 130`

`t_26 =-105`

Find which number of term has the value of `-60` in the sequence.

`-60 = 25 - 5n`

`-85 = -5n`

`17 = n`

Practice exercises:

1. Consider the following sequence: `4, 11, 18, ...`

a) Find the explicit formula
b) Find the 37th term
c) Find the value of `n` if the term has a value of `74`

Good luck!