The marble counts represent the sum of the first 25 natural numbers. Using the sum formula Sn = n(n + 1) / 2 with n = 25, the total calculation is 25 x 26 / 2, which gives 325 marbles.
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?
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The number of marbles in the rows forms the sequence 1, 2, 3, …, 25.
The total number of marbles used is the sum of the first 25 natural numbers:
S = 1 + 2 + 3 + … + 25.
Using the formula for the sum of the first n natural numbers:
Sn = n(n + 1) / 2
For n = 25:
S25 = 25 x (25 + 1) / 2
S25 = 25 x 26 / 2
S25 = 25 x 13 = 325.
Thus, the child uses a total of 325 marbles.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-8/