Question

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

Answer 1

The sequence will be: `T_n = a-4.5n+4.5`

Explanation:

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

`T_n =a+(n-1)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+(n-1)(-4.5)`

Simplifying gives: `T_n = a-4.5n+4.5`

The summation of all the terms will be:

`S_n =n/2(2a+(n-1)d)` where `d` is the common difference.

In your question `d=-4.5`.