Question

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

Answer 1

`d=(a_n-a_1)/(n-1)`

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,

`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=(a_n-a_1)/(n-1)`

This is d's expression.