# What is the n th term for an AP with a common difference of -4.5?

Oct 30, 2016

#### Answer:

The sequence will be: ${T}_{n} = a - 4.5 n + 4.5$

#### Explanation:

We know the general equation for nth term of an A.P.series is

${T}_{n} = a + \left(n - 1\right) d$

where $a$ is the first term of the series and $d$ is the common difference.

Now for the common difference ($d = - 4.5$) the sequence will be:

${T}_{n} = a + \left(n - 1\right) \left(- 4.5\right)$

Simplifying gives: ${T}_{n} = a - 4.5 n + 4.5$

The summation of all the terms will be:

${S}_{n} = \frac{n}{2} \left(2 a + \left(n - 1\right) d\right)$ where $d$ is the common difference.

In your question $d = - 4.5$.