Find the 8th term in series? 2, 2, 12, 12, 30, 30, - - - - -

Key insight: the terms come in repeating pairs and are generated by a simple formula depending on whether the position is odd or even.

• Observe the pairs: 2, 2 ; 12, 12 ; 30, 30. Each pair repeats the same value.

• Pattern rule: for position n (starting at 1), if n is odd use n^2 + n; if n is even use n^2 - n.

• Verify a few terms: 1st = 1^2 + 1 = 2; 2nd = 2^2 - 2 = 2; 3rd = 3^2 + 3 = 12; 4th = 4^2 - 4 = 12; 5th = 5^2 + 5 = 30; 6th = 6^2 - 6 = 30.

Compute the 7th and 8th terms:

1. 7th term (n = 7, odd): 7^2 + 7 = 49 + 7 = 56.

2. 8th term (n = 8, even): 8^2 - 8 = 64 - 8 = 56.

Answer: 56