Question

The algebraic expression of the sum of term of an arithmetic sequence is n2+8n.the sum of continuous terms starting from the first of this sequence is found to be 240.write a second degree equation based on this statement

Answer 1

Answer:

ANSWER

Sequence is 1,4,7,10,.....

(a) a=1,d=4−1=3

t

n

=a+(n−1)d

⇒t

n

=1+(n−1)d

⇒t

n

=1+3n−3

⇒t

n

=3n−2 which is algebraic form of the given arithmetic sequence.

(b) t

n

=3n−2

⇒t

n

=3n−2

⇒3n=102

⇒n=34

⇒100 is the 34

th

term of the sequence.

(c) We know, t

n

=3n−2

Square of the term of this sequence

=(3n−2)

2

=9n

2

−12n+4

=9n

2

−12n+12−8

=3[3n−2)

2

−2]−2

Let k=[(3n−2)

2

−2]

Square of the term of this sequence =3k−2

Since square of the sequence is of the form =3k−2, therefore square of any term of the sequence is a term of this sequence.

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