Question 28 of 51intermediate🔧 ApplyNumerical3 marks

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?

Correct Answer

325

Exercise: Exercise Set 8.2 | Q: 7 | (Page 13)
For More Understanding

Explanation

The number of marbles in each row forms an arithmetic progression (AP) starting from 1 up to 25. The total number of marbles used is the sum of the first 25 terms of this AP, calculated using the standard sum formula S_n = n/2 [2a + (n-1)d].

Solution Steps

  1. Step 1: Identify the sequence of marbles as an arithmetic progression (AP) where the first term (a) = 1, common difference (d) = 1, and number of terms (n) = 25.

  2. Step 2: Write the formula for the sum of the first n terms of an AP: S_n = n/2 [2a + (n - 1)d].

  3. Step 3: Substitute the values into the formula: S_25 = 25/2 [2(1) + (25 - 1)1].

  4. Step 4: Simplify the expression: S_25 = 25/2 [2 + 24] = 25/2×262 \times 26.

  5. Step 5: Calculate the final value: S_25 = 25×1325 \times 13 = 325.

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