Question

Luis
3
(5)
Prove that the squares of all the terms of the arithmetic sequence
4, 7, 10, ... belong to the sequence.
no perfect​

Answer 1

1st of all thanks for posting a beautifull ques here!! ans below.::

ATP,

d = 7-4=3 ; a = 4 .

the squares are :: 16, 49, 100. we just hv to find the position of these nos. refering the same d and a i.e.3 &4 respectively ...

let the n th term be 16

a' = a + (n-1)d => 16 = 4 + (n-1) 3 => 12/3 =(n-1) => n= 5 ... therefor 16 is the 5th term of the ap..

now, let the m th term be 49

a" = a+(m-1)d =>49=4+(m-1) 3 => 45/3 = m-1 => m= 16... •°• 49 is the 16 term of the ap

again, let the s th term be 100

a "' = a + (s-1)d =>100=4+3(s-1) => 96/3=s-1 => s=33 ..•°• 100 is the 33 rd term of the ap

since, 16 is the 5th term ,49 is the 16 term and 100 is the 33 rd term ..therfore all r included in this ap hence the sum is proved... hope it will help...