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07-02-2017
Mathematics

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The first term of an arithmetic sequence is-3 and the 15 term is 53. What is the common difference of the sequence?

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LammettHash LammettHash

07-02-2017

[tex]a_2=a_1+d[/tex]
[tex]a_3=a_2+d=a_1+2d[/tex]
[tex]a_4=a_3+d=a_1+3d[/tex]
...
[tex]a_{15}=a_1+14d[/tex]

Since [tex]a_1=-3[/tex] and [tex]a_{15}=53[/tex], the common difference [tex]d[/tex] is

[tex]53=-3+14d\implies d=4[/tex]

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