Question

What is the next tern: 2,6,12,20,30,....................

Answer 1

Answer:

42

Step-by-step explanation:

2+4=6,6+6=12,12+8=20,20+10=30,30+12=42

Answer 2

*Answer:

1^1+1=2

2^2+2=6

3^2+3=12

4^2+4=20

5^2+5=30

nth term=n^2+n

Next number=6^2 +6=36+6=42

II method:

1*(1+1)=2

2*3=6

3*4=12

4*5=20

5*6=30

nth term=n*(n+1)

next no=6th term= 6*(6+1)=6*7=42

EDIT 1:

III METHOD:

0+2*1=2

2+2*2=6

6+2*3=12

12+2*4=20

20+2*5=30

Thus nth term

Tn=Tn-1+2*n Or Tn-Tn-1=2*n

So we can write

T2-T1=2*2

T3-T2=2*3

T4-T3=2*4

………………..

………………..

Tn-1-Tn-2=2*(n-1)

Tn-Tn-1=2*n

————————————————

Adding all we get

Tn-T1=2*(2+3+4+………………………….+n)

Tn=2*(1+2+3+4+………………………….+n)

=2*n(n+1)/2=n(n+1)

Tn=n(n+1)

which is same as above

Thus T6=T5+2*6=30+12=42

METHOD IV:

Tn=(n^3–1) /(n-1) - 1

Thus T3=(27–1)/(3–1)-1=26/2–1=13–1=12

T4=(64–1)/(4–1) -1 =63/3–1=21–1=20

T5=(125–1) / ( 5–1)-1=124/4–1=31–1=30

Next term=T6=(6^3–1)/(6–1) -1=(216–6)/(6–1) -1=215/5–1=43–1=42

EDIT 2:

METHOD V:

nth term=(n+1)(n-1) +n+1

T1=0*2+2=2

T2=1*3+3=6

T3=2*4+4=12

T4=3*5+5=20

T5=4*6+6=24+6=30

Next term T6=5*7+7=35+7=42

EDIT 3:

METHOD VI:

nth term=(n-1)^2 +3n-1

T4=(4–1)^2+3*4–1=9+12–1=20

T5=(5–1)^2 +3*5–1=16+15–1=30

Next term T6=(6–1)^2 +3*6–1=25+18–1=42

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