How do you write an arithmetic series for which s_5=10?

1 Answer
May 10, 2017

Here's a method...

Explanation:

Take any arithmetic series with at least 5 terms and non-zero sum to 5 terms, then multiply it by 10 / "sum".

For example:

1+2+3+4+5 = 15

So, multiplying by 10/15 = 2/3 we get:

2/3+4/3+6/3+8/3+10/3 = 10

For this example, the initial term is 2/3, the common difference 2/3 and the formula for the general term can be written:

a_n = 2/3+2/3(n-1)

or more simply:

a_n = 2/3n