MathDB

18

Part of 2015 AMC 8

Problems(1)

X Marks the Spot

Source: 2015 AMC 8 #18

11/25/2015
An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, 2,5,8,11,142,5,8,11,14 is an arithmetic sequence with five terms, in which the first term is 22 and the constant added is 33. Each row and each column in this 5×55\times5 array is an arithmetic sequence with five terms. What is the value of XX?
<spanclass=latexbold>(A)</span>21<spanclass=latexbold>(B)</span>31<spanclass=latexbold>(C)</span>36<spanclass=latexbold>(D)</span>40<spanclass=latexbold>(E)</span>42<span class='latex-bold'>(A) </span>21\qquad<span class='latex-bold'>(B) </span>31\qquad<span class='latex-bold'>(C) </span>36\qquad<span class='latex-bold'>(D) </span>40\qquad <span class='latex-bold'>(E) </span>42
[asy] size(3.85cm); label("XX",(2.5,2.1),N); for (int i=0; i<=5; ++i) draw((i,0)--(i,5), linewidth(.5));
for (int j=0; j<=5; ++j) draw((0,j)--(5,j), linewidth(.5)); void draw_num(pair ll_corner, int num) { label(string(num), ll_corner + (0.5, 0.5), p = fontsize(19pt)); }
draw_num((0,0), 17); draw_num((4, 0), 81);
draw_num((0, 4), 1);
draw_num((4,4), 25);
void foo(int x, int y, string n) { label(n, (x+0.5,y+0.5), p = fontsize(19pt)); }
foo(2, 4, " "); foo(3, 4, " "); foo(0, 3, " "); foo(2, 3, " "); foo(1, 2, " "); foo(3, 2, " "); foo(1, 1, " "); foo(2, 1, " "); foo(3, 1, " "); foo(4, 1, " "); foo(2, 0, " "); foo(3, 0, " "); foo(0, 1, " "); foo(0, 2, " "); foo(1, 0, " "); foo(1, 3, " "); foo(1, 4, " "); foo(3, 3, " "); foo(4, 2, " "); foo(4, 3, " ");
[/asy]
AMC 8AMCarithmetic sequence