Question

Consider the arithmetic sequence 5,9,13 ,..... .

a) What is its common difference ?

b) What is its algebraic form ?

c) Check whether the square of any term is a term of this sequence or not ?​

Answer 1

(a)Common difference = 9 - 5 = 4.

(b)Algebraic form =
Nth term = a + (n - 1)d
= 5 + (n - 1) x 4
= 5 + 4n - 4
4n + 1

(c) let n be any term.
Then according to statement
n^2 = 4n + 1
n^2 - 4n - 1 = 0
D = b^2 - 4ac = 16 + 4 = 20 which is not a perfect square, so roots of this equation are irrational.
Hence, there is no such term.

Answer 2

(a) Common difference is 4.

(b) Algebraic form : 4n + 1.

(c) No, the square of any term is not a term of this sequence.

Given,

An arithmetic sequence: 5, 9, 13...

To Find,

(a) Common difference.

(b) Algebraic form.

(c) Check whether the square of any term is a term of this sequence or not?

Solution,

(a) Common difference (d) = Succeeding term - Previous term

⇒ d = 9 - 5 = 4

(b) Algebraic form for nth term,

⇒ aₙ = a + (n - 1)d

⇒ aₙ = 5 + (n - 1)4

⇒ aₙ = 4n + 1

(c) For the square of any term in the sequence,

According to the question,

⇒ (4n + 1)² = 16n² + 8n + 1

This cannot be written as a + (n - 1)d.

So, the square of any term is not a term of this sequence.

Hence, (a) Common difference is 4.

            (b) Algebraic form : 4n + 1.

            (c) No, the square of any term is not a term of this sequence.

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