Question

prove that the square of any term of the arithmetic sequence 7,11,15 doesn't belong to the sequence​

Answer 1

Answer:

It is proved that the square of any term of the arithmetic sequence 7,11,15 doesn't belong to the sequence​.

Step-by-step explanation:

Given arithmetic sequence is 7,11,15

Here, a= 7

          d = 11-7 = 4

     Tₙ = a + (n-1)d

   Let Tₙ = 49 (7 square)

          49 = 7+ (n-1)4

          42 = (n-1) 4

            n-1 = 21/2

               n = 21/2 + 1

               n = 23/2

          But 'n' can not be a fractional/rational number.

             Therefore n=23/2 is impossible.

      It implies that 49 is not a term of the given AP.

Try these steps for 121 and 225 also. You will get it.