sequences 7

First Term: $1^{3}-1^{2}=0$ , Second Term: $2^{3}-2^{2}=4$ , Third Term: $3^{3}-3^{2}=18$ , Fourth Term: $4^{3}-4^{2}=48$ , Fifth Term: $5^{3}-5^{2}=100$

0,4,18,48

There difference is as follows:
4,14,30 There difference is as follows:
10,16 So there is a always a difference of 6 at this stage, we see the difference becomes 22
this implies the difference are 4,14,30,52
So after adding 52 to 48 we get 100

First Term:0=0×1^1, Second Term: 4 = 1×2^2, Third Term: 18 = 2×3^2, Fourth Term: 48 = 3×4^2 , Fifth Term:100 = 4×5^2 :)

0(1^2)= 0(1)=0 1(2^2)=1(4)=4 2(3^2)=2(9)=18 3(4^2)=3(16)=48 4(5^2)=4(25)=100

next term: 4(5^2) =4(25)= 100