Question

The first term of an arithmetic sequence is 5, and the tenth term is 13. Find the common difference

Answer 1

Common difference d when The first term of an arithmetic sequence is 5, and the tenth term is 13 is $d=\frac{8}{9}$

Step-by-step explanation:

The first term a₁ = 5

The tenth term a₁₀ = 13

Find Common difference d=?

The formula used for arithmetic sequence is:

$a_{n}=a_{1}+(n-1)d$

where aₙ = nth term

a₁= 1st term

d= common difference

Finding d:

$a_{10}=a_{1}+(n-1)d\\Putting\,\,values\,\,a_{10}=13, a_{1}=5 and n=10\\13=5+(10-1)d\\13-5=9d\\8=9d\\d=\frac{8}{9}$

So, Common difference d when The first term of an arithmetic sequence is 5, and the tenth term is 13 is $d=\frac{8}{9}$

Keywords: arithmetic sequence

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