Q2 of 50 Page 17

Look at these pictures.


If the pattern is continued, do the numbers of coloured squares from an arithmetic sequence? Give reasons.


No. of coloured squares in


Figure 1 – 8


Figure 2 – 12


Figure 3 – 16


As can be seen from the figures, the side of each coloured square increases linearly from 3,4,5… and so on. Hence, it is an AP


With common difference = 12-8 = 16-12 = 4


More from this chapter

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3

Look at these pictures –


The second picture is obtained by removing the small triangle formed by joining the midpoints of the first triangle. The third picture is got by removing such a middle triangle from each of the red triangles of the second picture.


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


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


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


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


process.

 1

Check whether each of the sequences given below is an arithmetic sequence. Give reasons.

For the arithmetic sequences, write the common difference also.


i) Sequence of odd numbers


ii) Sequence of even numbers


iii) Sequence of fractions got as half the odd numbers


iv) Sequence of powers of 2


v) Sequence of reciprocals of natural numbers

 3

See this pictures below –


i) How many small squares are there in each rectangle?


ii) How many large squares?


iii) How many squares in all?


Continuing this pattern, is each such sequence of numbers, an arithmetic sequence?

 4

In this picture, the perpendiculars to the bottom line are equally spaced. Prove that, continuing like this, the lengths of perpendiculars form an arithmetic sequence.