# Question #b65ad

##### 1 Answer

The

#### Explanation:

Examining the sequence, we find that the difference between successive terms increase by

As the difference increases by

#=(3+2(0))+(3+2(1))+...+(3+2(n-2))#

#=(3+3+...+3) + (2(0)+2(1) + ... + 2(n-2))#

#=3(n-1) + 2(1+2+...+(n-2))#

#=3(n-1)+2(((n-2)(n-1))/2)#

(The above comes from that the sum of all successive integers from

#=3(n-1)+(n-2)(n-1)#

#=(n-1)(n+1)#

Checking we find that this matches up with the given values. E.g. the