2013 AMC 12A Problems/Problem 7

Problem

The sequence $S_1, S_2, S_3, \cdots, S_{10}$ has the property that every term beginning with the third is the sum of the previous two. That is, $S_n = S_{n-2} + S_{n-1} \text{ for } n \ge 3.$ Suppose that $S_9 = 110$ and $S_7 = 42$ . What is $S_4$ ?

$\textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 16\qquad$

Solution

$S_9 = 110$ , $S_7 = 42$

$S_8 = S_9 - S_ 7 = 110 - 42 = 68$

$S_6 = S_8 - S_7 = 68 - 42 = 26$

$S_5 = S_7 - S_6 = 42 - 26 = 16$

$S_4 = S_6 - S_5 = 26 - 16 = 10$

Therefore, the answer is $\boxed{\textbf{(C) }{10}}$

Video Solution

https://youtu.be/CCjcMVtkVaQ ~sugar_rush

2013 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

2013 AMC 12A Problems/Problem 7

Contents

Problem

Solution

Video Solution

See also