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the formula to find a certain number in an arithmetic sequence is an=a1+d(n-1) where an represents the nth term of the sequence, a1 is the first term of the sequence, and d is the common difference. solve for d

Respuesta :

TaeKwonDoIsDead

Answer:

[tex]d=\frac{a_n-a_1}{n-1}[/tex]

Step-by-step explanation:

We need to do some algebraic manipulation to the formula to get our answer [solving for d]:

Note: we will first use distributive property  a(b+c) = ab + ac

Now,

[tex]a_n=a_1+d(n-1)\\a_n=a_1+dn-d\\a_n-a_1=dn-d\\a_n-a_1=d(n-1)\\d=\frac{a_n-a_1}{n-1}[/tex]

This is d's expression.

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