NCERT Solutions Ganita Prakash (Part 2) Chapter 6 .3 Number Pyramids — In-text Question

Book page 1406 Updated on2026-09-05

Q1.
What about a pyramid with three rows? Using letter numbers for the bottom row, we can write an expression for the top row.
Answer

With bottom row a, b, c the middle row is a + b and b + c, so the top is their sum:

(a + b) + (b + c) = a + 2b + c
a + 2b + ca + bb + cabc
Bottom a, b, c → middle a + b, b + c → top a + 2b + c.
Why it happens: b sits under both boxes of the middle row, so it is added twice on the way up, while a and c each feed only one box. The number in the middle of the bottom row therefore has twice the pull of the numbers at the ends — change b by 1 and the top changes by 2.
Check it yourself: take a = 1, b = 9, c = 4. The top should be 1 + 18 + 4 = 23 — and building it gives 10, 13 and then 23 ✓, exactly the pyramid printed on page 137.
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