2024/028)What is the next term in series 8, 15, 24, and 35 and find the general term

 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