The sum of squares of first n natural numbers is given by or Find the sum of squares of the first 10 natural numbers.

(i) A triangle is made up of 2 red sticks and 1 blue sticks . The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below:

(ii) In the given figure, the length of a green side is given by g and that of the red side is given by p.

Write an expression for the following pattern. Also write an expression if 100 such shapes are joined together.

The sum of first n natural numbers is given by Find

(i) The sum of first 5 natural numbers.

(ii) The sum of first 11 natural numbers.

(iii) The sum of natural numbers from 11 to 30.

The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of

(a) Table of 7

(b) Table of 10

(c) Table of 19

If = 2x + 3, x + 7 and = x – 3, then find the value of :

i.

ii.