If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 22?	Select.
A) 101  B) 187  C) 191  D) 201  E) 242
ok, not sure if this is the best explanation, but here is my way of solving this :   tn +1 = tn + n,   t 3 = 14   so:   t 4 = t 3 + 3   t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4   ....   so we get   t 22 = t 3 + 3 + 4 + 5 + 6....+ 21   the 3 + 4 + 5 + ... + 21 sequence is equal the sequence 1 + 2 + ... + 21, minus 1 + 2 at the beginning (so, minus 3)   and the 1 + 2 ... + 21 sequence is equal to n*(n+1)/2 with n being 21, so equal to  21 * 22 / 2= 
<gadget id="calculator"> 21 * 22 / 2</gadget>
<output>231</output>
231   so :   t 22= t 3 + 231 - 3   t 22 = 14 + 231 - 3 = 231 + 11= 
<gadget id="calculator">231 + 11</gadget>
<output>242</output>
242, hence answer 242
<result>E</result>
If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 22?