What is the 6th term of the sequence 2, 6, 12, 20, 30, ?

What is the 6th term of the sequence 2, 6, 12, 20, 30, ?

• A. 42
• B. 56
• C. 36
• D. 48

Answer: (A)

Each step is built by adding an even number that gets larger by 2 each time: 4, 6, 8, 10. The next difference should be 12, so the next term is 30 + 12 = 42. Therefore, the sixth term is 42. (Also, the sequence follows t_n = n(n+1), so t6 = 6×7 = 42.)

Each step is built by adding an even number that gets larger by 2 each time: 4, 6, 8, 10. The next difference should be 12, so the next term is 30 + 12 = 42. Therefore, the sixth term is 42. (Also, the sequence follows t_n = n(n+1), so t6 = 6×7 = 42.)