Question

Write the algebraic form of the arithmetic sequence 1,4,7,10…. a. Is 100 a term of this sequence? Why? b. Prove that the square of any term of this sequence belongs to that sequence​

Answer 1

(a) a=1,d=4−1=3tn=a+(n-1)d

tn=1+3n-3

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

(b) tn=3n-2

tn=3n-2

3n=102

n=34

100 is the 34th term of the sequence.

(c) we know tn=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.