Question

Solve the formula for a in the arithmetic series formula S = n*a + (n-1)h ?

Answer 1

To solve the formula S = n*a + (n-1)h for 'a', rearrange and isolate 'a' on one side to get a = (S + h)/n - h.

Step-by-step explanation:

The problem asks to solve for 'a' in the arithmetic series formula S = n*a + (n-1)h. To do this, we need to isolate 'a' on one side of the equation:

1. Rewrite the formula: S = na + nh - h.
2. Combine like terms: S = n(a + h) - h.
3. Isolate 'a': S + h = n(a + h).
4. Divide both sides by n: (S + h)/n = a + h.
5. Subtract h from both sides to solve for 'a': a = (S + h)/n - h.

This result gives us 'a' as a function of S, n, and h.