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Course: Algebra (all content) > Unit 18

Lesson 2: Arithmetic series
Math
Algebra (all content)
Series & induction
Arithmetic series
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Arithmetic series

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Walk through a guided practice where you'll start by finding a simple sum and end by evaluating finite arithmetic series.
Let's start with an addition problem.

Find the sum of 1+3+5+7+9.

  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Awesome! You just found the sum of a small arithmetic series. It only had 5 terms. But, what if it had one million terms? We'd want a formula for sure. Thankfully, we've already learned of such a formula.
Identify the formula for the sum of an arithmetic series.
صرف 1 جواب چنو

Sweet! So you remember the formula. Now let's make sure we remember how to apply it.
Choose the answer that shows the formula correctly used to find the sum you found.
صرف 1 جواب چنو

Alright, so we're feeling good so far. Let's try to use the formula to find the sum of an arithmetic series that would be tedious to calculate by hand.

Consider the series 3+5+7+…+401.

Find the values of a1 and an for this series.
a1=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
an=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Find the value of n for this series.
n=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Find the sum of 3+5+7+…+401
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Wow! Okay, looks like you've got this.

Try it yourself

Problem 1
Find the sum.
11+20+29+…+4052=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Nice! Try another one!
Problem 2
Find the sum.
10+(−1)+(−12)+…+(−10,979)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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