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2025 AMC 10A Problem 19

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2025 AMC 10A Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Sequences & Series · difficulty 3 of 5 · about 5 min · position P16-20

An array of numbers is constructed beginning with the numbers $-1\qquad3\qquad1$ in the top row. Each adjacent pair of numbers is summed to produce a number in the next row. Each row begins and ends with $-1$ and $1$ , respectively.

$\begin{array}{ccccccccc} &&-1&&3&&1&&\\ &-1&&2&&4&&1&\\ -1&&1&&6&&5&&1\\ \end{array}$

If the process continues, one of the rows will sum to $12,288$ . In that row, what is the third number from the left?

A)
$-29$
B)
$-21$
C)
$-14$
D)
$-8$
E)
$-3$

2025 AMC 10A Problem 19

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