Kerala Board Solutions for Chapter: Numbers and Algebra, Exercise 1: Exercise 1

Consider the following table:

Check whether we get $50$ at the top, or not.

Make a number pyramid by a set of four consecutive natural numbers. What is the relation between the starting number and the final number? What is the relation between the middle two numbers in the bottom row and the top most number? Explain this relation using algebra.

Complete the following table:

Explain the relation between the middle number in the bottom row and the topmost number using algebra.

Take any three consecutive natural numbers and add the first and last. Is there any relation between this sum and the middle number?

For any three consecutive natural numbers, the sum of the first and last is twice the middle one. Is this is true if we take three consecutive even numbers $2, 4, 6$?

For any three consecutive natural numbers, the sum of the first and last is twice the middle one. Is this is true if we take three consecutive odd numbers?

For any three consecutive natural numbers, the sum of the first and last is twice the middle one. Is this is true if we take three consecutive multiples of $3$?

For any three consecutive natural numbers, the sum of the first and last is twice the middle one. Is this is true if we added $1$ to the multiples of $4$?