We have the terms 8,15,24,35
Let us compute 1st order difference 7,9,11 which is an AP
Next difference is 13 and so next term is 35 + 13 = 48
So the nth term of the given sequence is quadratic say $an^2+bn + c$
Putting n =1 ,n= 2 and n =3 we get following
$a+b + c = 8\cdots(1)$
$4a+2b + c = 15\cdots(2)$
$9a+3b + c = 24\cdots(3)$
Subtracting (1) from (2) we get
$3a+b = 7\cdots(4)$
Subtracting (2) from (3) we get
$5a+b = 9\cdots(5)$
Subtracting (4) from (3) we get $2a=2$ or $a=1$
Putting $a=1$ in (4) we get $b=4$ and putting in (1) we get $c=3$
So $n^{th}$ term = $n^2+4n + 3$
we get the same results by putting n=1,2,3,4 so on
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