If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+4) for all positive integers n, what is the third term of the sequence? Pick.
A) 3	B) 4	C) 6	D) 8	E) 9
Tn = nth term   T1 = 1st term   T2 = 2nd term   and so on...   Sn = Sum of first n terms of the sequence   Sn = 1st term + 2nd term + 3rd term + ... + nth term   Sn = T1 + T2 + T3 + ....Tn   You are given here thatSn is the SUM of first n terms...So you have   Sn = T1 + T2 + T3 + ....Tn = n(n+1)   So S1 = T1   S2 = T1 + T2   S3 = T1 + T2 + T3   and so on   S1 = T1 = 1*(1+1)= 
<gadget id="calculator">1*(1+1)</gadget>
<output>2</output>
2   S2= T1 + T2 = 2 + T2 = 2*(2+1)= 
<gadget id="calculator">2*(2+1)</gadget>
<output>6</output>
6   So T2= 4   S3 = T1 + T2 + T3 = 2 + 4 + T3 = 3*(3+1)= 
<gadget id="calculator">3*(3+1)</gadget>
<output>12</output>
12   So T3= 9   (This is what we wanted)   The third term is 9.   9
<result>E</result>
If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+4) for all positive integers n, what is the third term of the sequence?