A sequence is defined recursively by a_1 = 4 and a_n = 2a_n-1 + 3. What is a_4?

Use the recursive rule term by term: $a_1=4$, then $a_2=2(4)+3=11$, then $a_3=2(11)+3=25$, then $a_4=2(25)+3=53$, choice C. Each term is found from the one before it, so none can be skipped. Choice A ($25$) stops one term early and is $a_3$. Choice D ($56$) adds $3$ before doubling, $2(25+3)$, instead of doubling first and then adding $3$. Choice B ($29$) uses addition, $25+4$, and ignores the doubling. Recursive sequences must be computed in order.