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