Question 545656: What is the differance in this sequence? 7,14,23,34,47,62,79,98,119,142,167,194! What is the nth number?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
7,14,23,34,47,62,79,98,119,142,167,194,...
We notice that if we add 2 to each of those we get this
familiar sequence of squares:
9,16,25,36,49,64,81,100,121,144,169,196,...
which equals
3²,4²,5²,6²,7²,8²,9²,10²,11²,12²,13²,14²,...
Connecting it with the sequence 1,2,3,...
(1+2)²,(2+2)²,(3+2)²,(4+2)²,(5+2)²,(6+2)²,(7+2)²,(8+2)²,(9+2)²,(10+2)²,(11+2)²,(12+2)²,
which has nth term (n+2)².
The original sequence has terms which are 2 less than the terms of this
sequence, so the nth term of the original sequence is (n+2)²-2 = n²+4n+4-2 or
n²+4n+2
So the nth number is n²+4n+2.
Edwin
|
|
|
