Series and Sequences 1 - nth terms

There are a few of these.

Let's just start with a definition. A sequence is a load of numbers in a list, with there being a common difference between the numbers.

A series is the same thing, but added together.

Here is an arithmetic sequence: 0,2,4,6,8,10....

Here is an arithmetic series: 0+2+4+6+8+10.....

In an arithmetic series or sequence, there is always a common difference between the numbers. In the ones above, the common difference is 2. It is always a constant (and not anything weird like n² - that's more like geometric series).

So finding the nth term of an arithmetic series or sequence is easy enough.

You need the first term a₁ and the common difference d.

a_n = a₁ + (n-1)d

So say I wanted to find the 42nd term of the above sequence.

a₄₂ = 0 + 41d
= 0 + 41x2
= 82

The 42nd term of the sequence 0,2,4,6,8...is 82


Because the difference is a constant with arithmetic sequences, this formula is simple enough to grasp. To find the nth term you need the first term, and then the number of terms before the nth one timesed by the common difference because there are that many lots of the common difference.