if b= a+(n-1)d, how do you solve for n?
start by getting all the n terms on one side, the rest on the other:
(n-1)d = b-a
then unwind the expressions till n is left alone:
n-1 = (b-a)/d
n = 1 + (b-a)/d
To solve for n in the equation b = a + (n - 1)d, you can follow these steps:
1. Start with the given equation: b = a + (n - 1)d.
2. Simplify the equation by distributing the value of d: b = a + nd - d.
3. Rearrange the equation by moving the term 'a' to the other side: b - a = nd - d.
4. Combine like terms: b - a = d(n - 1).
5. Divide both sides of the equation by d: (b - a) / d = n - 1.
6. Add 1 to both sides of the equation: (b - a) / d + 1 = n.
So the value of n can be obtained by taking (b - a) divided by d, and then adding 1 to the result.