Arithmetic and Geometric Sums

An arithmetic series adds a fixed constant $d$ to the previous term to get the next term.

$a_1 + a_2 + a_3 + \dots + a_n = a_1 + (a_1 + d) + (a_1 + 2d) + \dots + (a_1 + (n-1)d)$

The sum of $a_1$ through $a_n$ is

$S_n = \frac{n(2a_1 + (n-1)d)}{2}$

A geometric series multiplies the previous term by a fixed constant $r$ to get the next term.

$a_1 + a_2 + a_3 + \dots + a_n = a_1 + ra_1 + r^2 a_1 + \dots + r^{n-1} a_1$

The sum of $a_1$ through $a_n$ is

$S_n = a_1 \frac{r^n - 1}{r - 1}$

You are given the first three terms of a series that is either arithmetic or geometric. Compute the sum of its first $N$ terms. The first term has index 1, and the sum includes the $N$-th term.

The input holds several data sets, two lines each. The first line is $N$, the number of terms to sum. The second line is the first three terms of the series, integers separated by spaces. The series is either arithmetic or geometric. A line whose $N$ is zero ends the input, and no series line follows it. If the series is geometric, the ratio $r$ is an integer.

For each data set print $S_n$ on its own line. The sum can be larger than a 64-bit integer holds.

• $1 \le N \le 100$
• $1 \le a_1, a_2, a_3 \le 2500$