Question

If you have


`3^(n-1) *(n(n+1))/(2) = 20412`
whats the process for solving n?

Answer 1

Explanation:

3^(n-1) * (n(n+1)/2 = 20412

The n(n +1)/2 is a factorial which is defined for integers so we are looking for a whole number solution.

We could draw a graph manually or using software and get the solution where the graph cuts the x axis.

Also we could find the prime factors of 20412:

20412 = 2^2 * 3^6 * 7

and try substituting 2, 3 and 7 into the equation

Using this method we see that one solution is n = 7.

I could have tried n = 7 first because 3^n-1 = 3^6!!