Answer:
[tex]a_n=(n+1)(n+2)[/tex]
Step-by-step explanation:
Notice that the terms given in the sequence are the products of two consecutive numbers as follows:
[tex]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[/tex]
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:
[tex]a_n=(n+1)(n+2)[/tex]
