Find each sum. 2+4+6+⋯+70

Name: Problem 43, Chapter 11: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-05-09T01:47:52-08:00
Duration: 1 min 56 s
Channel: Julie Silva
Description: Find each sum. 2+4+6+⋯+70

step 1 So we're being asked to find the sum of this arithmetic series. Well, we know that A sub 1 is eq

Question

Find each sum. $$ 2+4+6+\cdots+70 $$

   Find each sum.
$$
2+4+6+\cdots+70
$$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 11, Problem 43

Instant Answer

Solved by Expert Julie Silva

05/09/2020

Step 1

The sequence given is $2, 4, 6, \ldots, 70$. This is an arithmetic sequence because the difference between consecutive terms is constant. The common difference $d$ is $4 - 2 = 2$. Show more…

Show all steps

Thanks for your feedback!

Find each sum. $$ 2+4+6+\cdots+70 $$

Play audio

Feedback

Julie Silva and 91 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a series of numbers in which each term after the first is obtained by adding a constant difference. This pattern provides a predictable structure, allowing for the use of specific formulas to find individual terms or sums, making it a fundamental concept in algebra and number theory.

Common Difference

The common difference is the constant amount you add to each term to get the next term in an arithmetic sequence. Recognizing the common difference simplifies the process of identifying terms in the sequence and aids in determining the sum or other properties of the series.

Arithmetic Series Sum Formula

The sum of an arithmetic series can be efficiently calculated using a formula that involves the number of terms and the average of the first and last terms. This method eliminates the need to add each term individually and is widely applicable in problems involving evenly spaced numbers.

Please give Ace some feedback