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

Apr 12, 2016

To find the explicit formula for an arithmetic sequence you must use the formula ${t}_{n} = a + \left(n - 1\right) d$.

#### 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

${t}_{n} = 20 + \left(n - 1\right) \times - 5$

${t}_{n} = 20 - 5 n + 5$

${t}_{n} = 25 - 5 n$

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.

${t}_{26} = 25 - 5 \times 26$

${t}_{26} = 25 - 130$

${t}_{26} = - 105$

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

$- 60 = 25 - 5 n$

$- 85 = - 5 n$

$17 = n$

Practice exercises:

1. Consider the following sequence: $4 , 11 , 18 , \ldots$

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!