How to Solve Arithmetic Sequences? (+FREE Worksheet!)
Do you want to know how to solve Arithmetic Sequences problems? you can do it in few simple and easy steps.
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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: xn=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. a17=38,d=3
Solution:
First, we need to find a1 or a. Use arithmetic sequence formula: xn=a+d(n−1)
If a8=38, then n=8. Rewrite the formula and put the values provided:
xn=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
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Arithmetic Sequences – Example 2:
Given the first term and the common difference of an arithmetic sequence find the first five terms. a1=18,d=2
Solution:
Use arithmetic sequence formula: xn=a+d(n−1)
If n=1 then: x1=18+2(1)→x1=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. a1=24,d=2
Solution:
Use arithmetic sequence formula: xn=a+d(n−1)
If n=1 then: x1=22+2(1)→x1=24
First five terms: 24,26,28,30,32
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Arithmetic Sequences – Example 4:
Find the first five terms of the sequence. a17=152,d=4
Solution:
First, we need to find a1 or a. Use arithmetic sequence formula: xn=a+d(n−1)
If a17=152, then n=17. Rewrite the formula and put the values provided:
xn=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.
- a1=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}
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