Q4 of 50 Page 17

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.



In Δ fab , Δ gac , and so on…


The subtended angle θ is same


∴ tanθ = constant


∴


Now l(ab)=l(bc)=l(cd)… given


∴ l(ac)=2× l(ab)


l(ad)= 3× l(ab)


For, tanθ = constant


l(gc)=2× l(fb)


l(hd)=3× l(fb)


Hence, lengths fb,gc,hd…are in AP


i.e. the length of perpendiculars are in AP.


More from this chapter

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2

Look at these pictures.


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

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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?

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The algebraic expression of a sequence is.

Xn = n3 – 6n2+ 13n – 7


Is it an arithmetic sequence?

 1

In each of the arithmetic sequences below, some terms are missing and their positions are marked with ∘. Find them.

i) 24, 42, ∘, ∘, … ii) ∘, 24, 42, ∘, …


iii) ∘, ∘, 24, 42, … iv) 24, ∘, 42, ∘, …


v) ∘, 24, ∘, 42, … vi) 24, ∘, ∘, 42, …