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

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Answer 1 · 2017-05-10T21:20:53

Here's a method...

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#