2017 AMC 10A Problems/Problem 1
Problem
What is the value of ?
Solution
Notice this is the term in an arithmetic sequence, such that:
\[\begin{split} a_1 = 3.\\ a_n = 2a_(n-1) + 1.\\ a_2 = 3*2 + 1 = 7.\\ a_3 = 7 *2 + 1 = 15.\\ a_4 = 15*2 + 1 = 31.\\ a_5 = 31*2 + 1 = 63.\\ a_6 = 63*2 + 1 = \boxed{\textbf{(C)}\ 127.} \end{split}\] (Error compiling LaTeX. Unknown error_msg)