# How do you find the explicit formula for the following sequence 3,1, -1,-3, -5?

Apr 19, 2017

${n}_{t h}$ term ${a}_{n}$ is $5 - 2 n$

#### Explanation:

Observe carefully, the difference of each term from its immediately preceding term is always constant, as

$1 - 3 = - 2$

$- 1 - 1 = - 2$

$\left(- 3\right) - \left(- 1\right) = - 3 + 1 = - 2$ and

$- 5 - \left(- 3\right) = - 5 + 3 = - 2$

Hence,it is an arithmetic sequence with first term as ${a}_{1} = 3$ and common difference $d = - 2$. Hence ${n}_{t h}$ term ${a}_{n}$ is given by

a_n=a_1+(n-1)×d

= 3+(n-1)×(-2)

= $3 - 2 n + 2$

= $5 - 2 n$