**Sum of Series: 1 2 5 12 25 46**

The given series does not follow a particular pattern. However, we can still find the sum of the series by using the formula for the sum of an arithmetic series.

***Arithmetic Series***

An arithmetic series is a sequence of numbers in which each term after the first is obtained by adding a constant value to the previous term. The constant value is called the common difference and is denoted by d. The sum of the first n terms of an arithmetic series is given by the formula:

Sn = n/2(2a + (n-1)d)

where a is the first term of the series, d is the common difference, and n is the number of terms in the series.

***Finding a, d and n***

In order to find the sum of the given series, we need to find the first term (a), common difference (d), and the number of terms (n).

From the given series, we can see that:
- a = 1
- The common difference is not constant, i.e., it changes after every term. Therefore, we need to find the differences between consecutive terms to find the common difference.
- n is not given. Therefore, we need to find it.

The differences between consecutive terms are:
- 2 - 1 = 1
- 5 - 2 = 3
- 12 - 5 = 7
- 25 - 12 = 13
- 46 - 25 = 21

From the above differences, we can see that the common difference is not constant. However, we can see that the differences themselves follow an arithmetic series with a common difference of 2.

Therefore, the second difference is:
- 3 - 1 = 2
- 7 - 3 = 4
- 13 - 7 = 6
- 21 - 13 = 8

From the above differences, we can see that the second difference is constant. Therefore, we can conclude that the given series is a quadratic sequence.

We can find the nth term of the series by using the formula for the nth term of a quadratic sequence:

an = a + (n-1)d + (n-1)(n-2)/2 * c

where c is the second difference.

Substituting the values, we get:

an = 1 + (n-1)1 + (n-1)(n-2)/2 * 2
an = n^2 - n + 1

We can now find the number of terms (n) by solving the quadratic equation:

n^2 - n + 1 = an
n^2 - n + 1 - an = 0

Using the quadratic formula, we get:

n = (1 ± √(1 - 4(1-an)))/2

Since n is a positive integer, we take the positive root:

n = (1 + √(1 - 4(1-an)))/2

Substituting the value of an, we get:

n = (1 + √(1 - 4(1-46)))/2
n = 6

Therefore, the number of terms in the series is 6.

***Finding the Sum***

Now that we have found a, d, and n, we can