# Look at these pic

i) How many red triangles are there in each picture?

In 1st picture, 1 red triangle

In 2nd picture, 3 red triangles

In 3rd picture, 9 red triangles

S1 = 1, 3, 9…

ii) Taking the area of the first triangles as 1, compute the area of a small triangle in each

picture.

In 2nd picture, each triangle is divided into 4 parts in which there are 3 red and 1`white triangle.

Hence, area of each small triangle = (1÷ 4) = 0.25 sq. units

In 3rd picture, each smaller triangle from the 2nd figure, except the middle triangle is further divided into further 4 equal parts.

Hence, area of each small triangle = (0.25/4) = 0.625 sq. units

S2 = 1, 0.25, 0.625…

iii) What is the total area of all the red triangles in each picture?

In 1st triangle, only red triangle is present.

In 2nd triangle, 3 red and 1 white triangle is present each of equal areas = 0.25 sq. units

Area of red triangles = 3 × 0.25 = 0.75 sq. units

In 3rd picture, each smaller triangle from the 2nd figure, except the middle triangle is further divided into further 4 equal parts.

Area of all red triangles = 9 × 0.0625 = 0.5625

S3 = 1, 0.75, 0.5625…

iv) Write the algebraic expressions for these three sequences obtained by continuing this process.

For 1st question, the sequence is 1, 3, 9…

Hence, the expression is 3n-1 , where n = 1,2,3…and so on

For 2nd question, the sequence is 1, 0.25, 0.625…

Hence, the expression is (1÷4) (n-1) = (0.25)n-1 ,where n = 1, 2, 3… and so on

For 3rd question, the sequence is 1,0.75,0.675…

Here, the expression is product of above 2 expressions

i.e. 3n-1 × 0.25n-1 = 0.75n-1

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