Question

Nth term of 6 12 20 30 42 56 72​

Answer 1

72, 90, 110, 132, 156

Explanation:

The pattern goes, (56+16), (72+18), (90+20), (110+22), (132+24), (156+26), etc.

With the beginning pattern of +6, add +2 to each +6 for the following numbers.

Answer 2

`a_n=(n+1)(n+2)`

Explanation:

Notice that the terms given in the sequence are the products of two consecutive numbers as follows:

`a_1=6=2*3\\a_2=12=3*4\\a_3=20=4*5\\a_4=30=5*6\\a_5=42=6*7\\a_6=56=7*8\\a_7=72=8*9`

Therefore, we can write the nth term of the sequence as the product of a number and its consecutive, starting with the factor "2" for the first term instead of "1", thus making:

`a_n=(n+1)(n+2)`