Question

Find the sum of the first forty terms of the arithmetic series -1/4+-7/12+-11/12+-5/4+-19/12+...

Answer 1

First, find the common difference. It should be -7/12 - (-1/4), or -7/12+1/4=-7/12+3/4=-4/12=-1/3.

Answer 2

Now that we have the difference, we need the last term. Do you remember the formula for a term in an arithmetic sequence?

Answer 3

OK then. It is \[a _{n}=a _{1}+d(n-1)\]

Answer 4

So, we're looking for the fortieth term. So our a40 is -1/4 + -1/3(39).

Answer 5

Which is -53/4.

Answer 6

Now, the sum of an arithmetic series is \[\frac{ n }{ 2 }(a _{n}-a _{1})\]

Answer 7

So we want 40/2 times -53/4 - (-1/4)=20(-52/4)=-52*5=-260.