Question

Consider the arithmetic sequence with first term and common difference. Is 1 a term of this sequence? What about 2?

Write the algebraic form of this sequence. Prove the no natural number occurs is this sequence.

Answer 1

First term of an arithmetic sequence = a + b =

Common difference = a =

Let 1 be the n^th term of the given sequence.

As n must be a natural number, 1 is not a term of this sequence.

Now, let 2 be the m^th term of the given sequence.

As n must be a natural number, 2 is not a term of this sequence.

Algebraic form of the sequence is

Let p, a natural number be the n^th term of the given sequence.

_{Therefore, for any value of p, n cannot be a natural number.}

Thus, no natural number occurs in this sequence.