Q5 of 50 Page 17

The algebraic expression of a sequence is.

Xn = n3 – 6n2+ 13n – 7


Is it an arithmetic sequence?

For it to be an AP, xn+1 – xn = constant


xn+1-xn = {(n+1)3-6(n+1)2+13(n+1)-7}-{ n3 – 6n2+ 13n – 7}


= (n+1)3-n3-6{(n+1)2-n2}+13(n+1-n)-7+7


= (n+1-n)(n2+2n+1+n2+n+n2)-6(2n+1)+13


= 1× (3n2+3n+1)-12n+7


= 3n2-9n+8


Which is not independent of n. Hence, the sequence is not an AP.


More from this chapter

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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.


 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, …

 2

The terms in two positions of some arithmetic sequences are given below. Write the first five terms of each:

i) 3rd term 34


6th term 67


ii) 3rd term 43


6th term 76


iii) 3rd term 2


5th term 3


iv) 4th term 2


7th term 3


v) 2nd term 5


5th term 2