Subject: Sum of an arithmetic series
Name: Jillian
Who are you: Other

Find the sum of 21 terms of an arithmetic series that has an eleventh term equal to 30.

 

Hi Jillian,

You are missing a piece of information. There are many different arithmetic series with eleventh term equal to 30. Here are two

20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

25, 25 1/2, 26, 26 1/2, 27, 27 1/2, 28, 28 1/2, 29, 29 1/2, 30

Penny

Hi again Jillian,

Sue wrote to me and pointed out that I read your problem incorrectly. There are many different arithmetic series with eleventh term equal to 30 but you asked for the sum not the terms in the sequence. Here is Sue's answer to your question.

Penny

Hi Jillian.

The eleventh term of a 21 term sequence is the middle term. In an arithmetic sequence, the differences between consecutive terms is constant (we often call this constant k). So your sequence is

{ 30-10k, 30-9k, 30-8k, ... ,30-k, 30, 30+k, ... 30+9k, 30+10k }

If you add them, the k terms cancel.

Hope this helps,
Stephen La Rocque.