2017 AMC 10A Problems/Problem 1

Problem

What is the value of $(2(2(2(2(2(2+1)+1)+1)+1)+1)+1)$ ?

$\textbf{(A)}\ 70\qquad\textbf{(B)}\ 97\qquad\textbf{(C)}\ 127\qquad\textbf{(D)}\ 159\qquad\textbf{(E)}\ 729$

Solution

Notice this is $a_6$ arithmetic sequence $a_1 = 3, a_n = 2a_(n-1) + 1.$ \\ $a_2 = 3*2 + 1 = 7.$ \\ $a_3 = 7 *2 + 1 = 15.$ \\ $a_4 = 15*2 + 1 = 31.$ \\ $a_5 = 31*2 + 1 = 63.$ \\ $a_6 = 63*2 + 1 = \boxed{\textbf{(C)}\ 127.}$

Page

Toolbox

Search

2017 AMC 10A Problems/Problem 1

Problem

Solution