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The question shown in the image asks about how many grains of rice are on a chessboard, where the number of grains increases from 1 on the first square, to 2 on the second square, to 3 on the third square, continuing up to 64 grains on the 64th square.

This appears to be a variation of the famous "Wheat and Chessboard" problem, but in this version, the number of grains of rice increases linearly by 1 for each successive square (1, 2, 3, 4,...).

### Calculation:
The sum of grains on the chessboard can be calculated as the sum of an arithmetic series where the first term \(a = 1\), the number of terms \(n = 64\), and the common difference \(d = 1\). The sum \(S_n\) of an arithmetic series is given by the formula:

\[
S_n = \frac{n}{2} \times (a + l)
\]

Where:
- \(n = 64\) (the number of squares),
- \(a = 1\) (grains on the first square),
- \(l = 64\) (grains on the last square).

Plugging in the values:

\[
S_{64} = \frac{64}{2} \times (1 + 64) = 32 \times 65 = 2080
\]

So, the total number of grains of rice is **2080**.

The correct answer is **D. 2080**.

Would you like further details or have any other questions? Here are some related questions:

1. What is the difference between an arithmetic and a geometric series?
2. How do you calculate the sum of a geometric series?
3. How would the problem change if the number of grains doubled on each square instead of increasing by 1?
4. Can this sum formula be applied to other situations, such as calculating distances or costs?
5. What is the general formula for an arithmetic progression, and how can it be adapted for different starting values and increments?

**Tip**: Arithmetic progressions are useful for many everyday calculations, such as budgeting and planning tasks that follow a regular pattern!

If I put one grain of rice on the first square of a chess board, two on the second, three on the third, and so on up to 64 grains on the 64th square, how many grains of rice are on the chess board?

Learn how to calculate the total number of grains of rice on a chessboard using arithmetic series, where grains increase linearly from 1 on the first square to 64 on the 64th. This problem explores the concept of arithmetic progression and is ideal for high school students.

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