# How do you write the nth term rule for the arithmetic sequence with d=-4.1 and a_16=48.2?

Mar 17, 2017

${a}_{n} = 113.8 - 4.1 \times n$

#### Explanation:

In an arithmetic sequence, whose first term is ${a}_{1}$ and common difference is $d$, the n^(th term ${a}_{n}$ is given by ${a}_{n} = {a}_{1} + \left(n - 1\right) d$

As ${a}_{16} = 48.2$ and $d = - 4.1$, we should have

$48.2 = {a}_{1} + \left(16 - 1\right) \times \left(- 4.1\right)$

or $48.2 = {a}_{1} + 15 \times \left(- 4.1\right)$

or $48.2 = {a}_{1} - 61.5$

and ${a}_{1} = 48.2 + 6.5 = 109.7$

Hence n^(th term rule for ${a}_{n}$ is ${a}_{n} = {a}_{1} + \left(n - 1\right) d$

i.e. ${a}_{n} = 109.7 + \left(n - 1\right) \times \left(- 4.1\right) = 109.7 - 4.1 \times n + 4.1$

i.e. ${a}_{n} = 113.8 - 4.1 \times n$