Arithmetic Sequence

Problem Level: 3

Find the sum of the arithemetic sequence -2, 4, 10 ... 100.

Solution:

The sum of any arithmetic sequence is the number of numbers in the sequence times the average of the sequence. 

The average (arithmetic mean) of the sequence is very easy to find.

(-2 +100 ) /2

=98/2

=49

The average of the sequence is 49.

To find the number of terms can be a bit more challenging.

Because the common difference is 6, try to make the first term 6.

We can do this by adding eight.  The new sequence is  6, 12 ,18 ...108

Dividing each term by 6 leaves us with: 1,2,3... 53.

This shows that there are 53 numbers in this sequence

53 x 49 = 2597

Answer: The sum of the sequence is 2597

We used counting techniques and arithmetic mean to solve this problem.  Most problems require many types of math to solve.