Q3 of 50 Page 17

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?

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


→ No. of small squares in


Rectangle 1 - 2


Rectangle 2 - 4


Rectangle 3 - 6


Rectangle 4 - 8


As is evident, it forms an AP with common difference = 4-2 =2


ii) How many large squares?


→ No. of large squares in


Rectangle 1 - 0


Rectangle 2 - 1 (intersection of all 4 small squares)


Rectangle 3 - 2 (2 same size overlapping squares as in rectangle 2)


Rectangle 4 - 3


As is evident, it forms an AP with common difference = 1-0 =1


iii) How many squares in all?


→ All squares = small squares + large squares


No. of all squares in


Rectangle 1 - 2 + 0 = 2


Rectangle 2 - 4 + 1 = 5


Rectangle 3 - 6 + 2 = 8


Rectangle 4 - 8 + 3 = 11


As is evident, it forms an AP with common difference = 2+1 = 3


More from this chapter

All 50 →
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

 2

Look at these pictures.


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

 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.


 5

The algebraic expression of a sequence is.

Xn = n3 – 6n2+ 13n – 7


Is it an arithmetic sequence?