# Arithmetic series

1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following:

a) What is d, the difference between any 2 terms?

b)

Using the formula for the nth term of an arithmetic sequence, what is 101st term?

c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?

d) Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?

e) What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?

https://brainmass.com/math/algebra/arithmetic-series-82943

#### Solution Preview

ARITHMETIC 1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following:

a) What is d, the difference between any 2 terms?

d=4-2=6-4=8-6=2

b)

Using the formula for the nth term of an arithmetic sequence, what is 101st term?

Use a formula

a(n)=a(1)+(n-1)d

we have

a(101)=a(1)+100d=2+100*2=202

c) ...

#### Solution Summary

This provides examples of working with an arithmetic series.