How to Solve Arithmetic Sequences? (+FREE Worksheet!)

Related Topics

• How to Solve Finite Geometric Series
• How to Solve Infinite Geometric Series
• How to Solve Geometric Sequences

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

Arithmetic Sequences – 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: \(32,35,38\)

The Absolute Best Books to Ace Pre-Algebra to Algebra II

The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Arithmetic Sequences – 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: \(18,20,22,24,26\)

Arithmetic Sequences – 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: \(24,26,28,30,32\)

The Best Book to Help You Ace Pre-Algebra

Pre-Algebra for Beginners The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

Arithmetic Sequences – 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 \(\color{blue}{: –38, –138, –238, –338, –438, Explicit: a_{n} = 62 – 100n}\)

The Greatest Books for Students to Ace the Algebra

Pre-Algebra Exercise Book A Comprehensive Workbook + PreAlgebra Practice Tests

Download

$29.99 Original price was: $29.99.$16.99Current price is: $16.99.