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 24?
Choose the correct choice from the following answers:
A) 101
B) 187
C) 191
D) 201
E) 287
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 24 = t 3 + 3 + 4 + 5 + 6....+ 23   the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3)   and the 1 + 2 ... + 23 sequence is equal to n*(n+1)/2 with n being 23, so equal to  23 * 24 / 2= 
<gadget id="calculator"> 23 * 24 / 2</gadget>
<output>276</output>
276   so :   t 20= t 3 + 276 - 3   t 20 = 14 + 276 - 3 = 276 + 11= 
<gadget id="calculator">276 + 11</gadget>
<output>287</output>
287, hence answer 287
<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 24?