Multiplication Sums 7D37D6
1. The problem is to find the sums of multiplication tables from 12 to 19.
2. The multiplication table for a number $n$ is the set of products $n \times 1, n \times 2, \ldots, n \times 10$.
3. To find the sum of the multiplication table for a number $n$, we use the formula for the sum of the first 10 natural numbers multiplied by $n$:
$$\text{Sum} = n \times (1 + 2 + \cdots + 10)$$
4. The sum of the first 10 natural numbers is:
$$1 + 2 + \cdots + 10 = \frac{10 \times (10 + 1)}{2} = 55$$
5. Therefore, the sum of the multiplication table for $n$ is:
$$\text{Sum} = n \times 55$$
6. Now, calculate the sums for $n = 12$ to $19$:
- For $12$: $12 \times 55 = 660$
- For $13$: $13 \times 55 = 715$
- For $14$: $14 \times 55 = 770$
- For $15$: $15 \times 55 = 825$
- For $16$: $16 \times 55 = 880$
- For $17$: $17 \times 55 = 935$
- For $18$: $18 \times 55 = 990$
- For $19$: $19 \times 55 = 1045$
These are the sums of the multiplication tables from 12 to 19.