Find fifth term.

2 = 1(1+1)

6=2(2+1)

12 = 3(3+1)

20=4(4+1)

so 5(5+1) = 30.

the sequence---------2...........6............12.......20.........

so, difference.................4............6...........8..........

so, the next difference will be 10 and the next term will be= $20+10=30$

see the difference between the nos. its a multiple of 2. 6 - 2= 4(2 2),12 - 6=6(2 3), 20-12=8(2 4) next woule be 2 5=10 hence 20+10=30

FIfth term is $5×6 = \color{#69047E}{\boxed{30}}$ .

It goes up in multiples of 2. Between 2 and 6 it 4 and between 6 and 12 is 6 and so on. So after 20 the next multiple is 10. So 20+10=30

see that the square of 2, minus 2 is the 1st term, then the square of 3, minus 3, is the 2nd term, the suare of 4 minus 4 is the 3d term, and so on, so the next term in the sequence is the same as the square of 6, minus 6 that is the same as 30

1^2+1=2 , 2^2+2=6, 3^2+3=12, 4^2+4=20, and hence the next number in the sequence will be 5^2+5=25+5=30

2+4=6 6+6=12 12+8=20 IN THIS ALL EVEN NOS. ARE ADDED FROM 4 ,4,6,8 THEN 10 WILL BE ADDED. 20+10=30

6-2=4,12-6=6(4+2),20-12=8(4+2+2),30-20=10(4+2+2+2)