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)