A child arranges marbles in rows so that the first row has 1 marble, the second has 2 marbles, the third has 3, and so on up to 25 rows. How many marbles does the child use in all?                                                             [Page No. 186]

Total marbles: $1 + 2 + 3 + \dots + 25$

Using the formula:

$$S = \frac{n(n+1)}{2}$$

$$S = \frac{25 \times 26}{2}$$

$$S = 25 \times 13 = 325$$

The child uses 325 marbles in all.

Concept Applied
The sum of the first n natural numbers is $\frac{n(n+1)}{2}$, useful in marble-arrangement and similar counting problems.