Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2017 AMC 10A Problems/Problem 1"

(Created page with "==Problem== What is the value of <math>(2(2(2(2(2(2+1)+1)+1)+1)+1)+1)</math>? <math>\textbf{(A)}\ 70\qquad\textbf{(B)}\ 97\qquad\textbf{(C)}\ 127\qquad\textbf{(D)}\ 159\qqua...")
 
(Solution to problem 1)
Line 4: Line 4:
  
 
<math>\textbf{(A)}\ 70\qquad\textbf{(B)}\ 97\qquad\textbf{(C)}\ 127\qquad\textbf{(D)}\ 159\qquad\textbf{(E)}\ 729</math>
 
<math>\textbf{(A)}\ 70\qquad\textbf{(B)}\ 97\qquad\textbf{(C)}\ 127\qquad\textbf{(D)}\ 159\qquad\textbf{(E)}\ 729</math>
 +
 +
 +
==Solution==
 +
 +
Notice this is <math>a_6</math> arithmetic sequence <math>a_1 = 3, a_n = 2a_(n-1) + 1.</math>\\
 +
<math>a_2 = 3*2 + 1 = 7.</math>\\
 +
<math>a_3 = 7 *2 + 1 = 15.</math>\\
 +
<math>a_4 = 15*2 + 1 = 31.</math>\\
 +
<math>a_5 = 31*2 + 1 = 63.</math>\\
 +
<math>a_6 = 63*2 + 1 = \boxed{\textbf{(C)}\ 127.}</math>

Revision as of 14:17, 8 February 2017

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10A_Problems/Problem_1&oldid=82788"