Question

prove that the squares of all the terms of the arithmetic sequence 4,7,10....belong to the sequence

Answer 1

Answer:

Proved

Step-by-step explanation:

prove that the squares of all the terms of the arithmetic sequence 4,7,10....belong to the sequence

AP is

4 , 7  , 10 ....

a = 4   d = 3

nth term  = a +(n-1)d =  4 + (n-1)3  = 4 + 3n - 3 =  3n + 1

square of nth Term =  (3n + 1)²

= 9n² + 6n + 1

= 3(3n² + 2n)  + 1

3n² + 2n = k

= 3k + 1

square of nth Term  = kth Term    where k = 3n² + 2n

Hence proved that the squares of all the terms of the arithmetic sequence 4,7,10....belong to the sequence

Answer 2

Answer:

Step-by-step explanation:

Sequence = 4,7,10 (Given)

Following the AP

Ap of 4 , 7  , 10 ....

where a = 4   d = 3

nth term  = a +(n-1)d

=  4 + (n-1)3  

= 4 + 3n - 3

=  3n + 1

Square of the nth Term = (3n + 1)²

= 9n² + 6n + 1

= 3 (3n² + 2n)  + 1

= 3n² + 2n = k

= 3k + 1

Square of nth Term  = kth Term  ( where k = 3n² + 2n)

Therefore, the squares of all the terms of the arithmetic sequence 4,7,10....belong to the sequence.