Arithmetic Sequences

Arithmetic Sequences

Do you want to know how to solve Arithmetic Sequences problems? you can do it in few simple and easy steps.

Step by step guide to solve Arithmetic Sequences problems

  • A sequence of numbers such that the difference between the consecutive terms is constant is called arithmetic sequence. For example, the sequence \(6, 8, 10, 12, 14\), … is an arithmetic sequence with common difference of \(2\).
  • To find any term in an arithmetic sequence use this formula: \(\color{blue}{x_{n}=a+d(n-1)}\)
  • \(a =\) the first term,\(d =\) the common difference between terms, \(n =\) number of items

Example 1:

Find the first three terms of the sequence. \(a_{17}=38,d=3\)

Solution:

First, we need to find \(a_{1}\) or a. Use arithmetic sequence formula: \(\color{blue}{x_{n}=a+d(n-1)}\)
If \(a_{8}=38\), then \(n=8\). Rewrite the formula and put the values provided:
\(x_{n}=a+d(n-1)→38=a+3(3-1)=a+6\), now solve for \(a\).
\(38=a+6→a=38-6=32\),
First three terms: \(32,35,38\)

Example 2:

Given the first term and the common difference of an arithmetic sequence find the first five terms. \(a_{1}=18,d=2\)

Solution:

Use arithmetic sequence formula: \(\color{blue}{x_{n}=a+d(n-1)}\)
If \(n=1\) then: \(x_{1}=18+2(1)→x_{1}=18\)
First five terms: \(18,20,22,24,26\)

Example 3:

Given the first term and the common difference of an arithmetic sequence find the first five terms. \(a_{1}=24,d=2\)

Solution:

Use arithmetic sequence formula: \(\color{blue}{x_{n}=a+d(n-1)}\)
If \(n=1\) then: \(x_{1}=22+2(1)→x_{1}=24\)
First five terms: \(24,26,28,30,32\)

Example 4:

Find the first five terms of the sequence. \(a_{17}=152,d=4\)

Solution:

First, we need to find \(a_{1}\) or \(a\). Use arithmetic sequence formula: \(\color{blue}{x_{n}=a+d(n-1)}\)
If \(a_{17}=152\), then \(n=17\). Rewrite the formula and put the values provided:
\(x_{n}=a+d(n-1)→152=a+4(17-1)=a+64\), now solve for \(a\).
\(152=a+64→a=152-64=88\),
First five terms: \(88,92,96,100,104\)

Exercises

Given the first term and the common difference of an arithmetic sequence find the first five terms and the explicit formula.

  • \(\color{blue}{a_{1} = 24, d = 2}\)
  • \(\color{blue}{a_{1} = –15, d = – 5}\)
  • \(\color{blue}{a_{1} = 18, d = 10}\)
  • \(\color{blue}{a_{1 }= –38, d = –100}\)

Download Arithmetic Sequences Worksheet

  • First Five Terms \(\color{blue}{: 24, 26, 28, 30, 32, Explicit: a_{n} = 22 + 2n}\)
  • First Five Terms \(\color{blue}{: –15, –20, –25, –30, –35, Explicit: a_{n} = –10 – 5n}\)
  • First Five Terms \(\color{blue}{: 18, 28, 38, 48, 58, Explicit: a_{n} = 8 + 10n}\)
  • First Five Terms \(\color{blue}{: –38, –138, –238, –338, –438, Explicit: a_{n} = 62 – 100n}\)

Related to "Arithmetic Sequences"

FREE Grade 8 MEAP Math Practice Test
FREE Grade 8 MEAP Math Practice Test
FSA Math Grade 7 Practice Test Questions
FSA Math Grade 7 Practice Test Questions
Top 10 Grade 4 MCAS Math Practice Questions
Top 10 Grade 4 MCAS Math Practice Questions
OST Grade 3 Math FREE Sample Practice Questions
OST Grade 3 Math FREE Sample Practice Questions
Grade 3 MAP Math Worksheets
Grade 3 MAP Math Worksheets
FREE Grade 8 MCAS Math Practice Test
FREE Grade 8 MCAS Math Practice Test
SBAC Math Grade 7 Practice Test Questions
SBAC Math Grade 7 Practice Test Questions
PSSA Math Grade 7 Practice Test Questions
PSSA Math Grade 7 Practice Test Questions
Top 10 Grade 4 PARCC Math Practice Questions
Top 10 Grade 4 PARCC Math Practice Questions
MCAS Grade 3 Math FREE Sample Practice Questions
MCAS Grade 3 Math FREE Sample Practice Questions

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…