Question

2, 6, 12, 20, 30, 42, 56,..
What is twelfth term of this series?

Answer 1

first term,a=2
common difference,d=6-2=4
we know, nth term=a+(n-1)d
therefore 12th term
=2+(12-1)4
=2+11*4
=2+44
=46
hence,the 12th term of the AP is 46

Answer 2

1 × 2 = 2

2 × 3 = 6

3 × 4 = 12

4 × 5 = 20

5 × 6 = 30

6 × 7 = 42

7 × 8 = 56

So the n-th term is n(n+1).

∴ 12th term = 12 × 13 = 156.

OR

1² + 1 = 1 + 1 = 2

2² + 2 = 4 + 2 = 6

3² + 3 = 9 + 3 = 12

4² + 4 = 16 + 4 = 20

5² + 5 = 25 + 5 = 30

6² + 6 = 36 + 6 = 42

7² + 7 = 49 + 7 = 56

So n-th term is n² + n.

[n(n + 1) = n² + n]

∴ 12th term = 12² + 12 = 144 + 12 = 156.

Thank you. Have a nice day. :-))

#adithyasajeevan