Answer
Yes. We can use the explicit formula below to find the nth term of an arithmetic sequence with a first term A(1) and a common difference d, by using the distributive property and by factoring out the common factor of d in the equation. Because: A(n) = A(1) + nd - d = A(1) + d (n - 1)
Work Step by Step
Yes. We can use the explicit formula below to find the nth term of an arithmetic sequence with a first term A(1) and a common difference d, by using the distributive property and by factoring out the common factor of d in the equation.
Given the equation
A(n) = A(1) + nd - d
We see that +nd and -d both have a common +d variable so we can factor out the +d from the two terms which gives us the equation.
A(n) = A(1) + d (n - 1)
And thus we can find the nth term of the sequence.
