Question

Prove that the arithmetic sequence 5,8,11,... contains on perfect squares. class 10 maths chapter 1 Arithmetic sequence.​ ​

Answer 1

Answer:

ANSWER

Explanation:

Answer and Explanation:

Prove that the arithmetic sequence 5, 8, 11 contains no perfect squares ?

Solution :

The arithmetic sequence 5, 8, 11.

Here, First term a=5

The common difference d=8-5=3

The nth term of the sequence is

a_n=a+(n-1)da

n

=a+(n−1)d

a_n=5+(n-1)3a

n

=5+(n−1)3

a_n=5+3n-3a

n

=5+3n−3

a_n=3n+2a

n

=3n+2

Let x be a natural number and its square is the nth term,

x^2=3n+2x

2

=3n+2

x^2-2=3nx

2

−2=3n

n=\frac{x^2-2}{3}n=

3

x

2

−2

Now, for all integers from 0 to 9, n does not come out to be an integer.

Therefore, the arithmetic sequence 5, 8, 11, … contains no perfect squares.