Question

A monument is built out of toothpicks. There are 25 rows and each row has eight more toothpicks than the row above. The top row has five toothpicks.

Part 1: How many toothpicks are on the bottom row? (4 points)

Part 2: Using complete sentences, explain the procedure taken to answer this question. (4 points)

Answer 1

u have 25 rows, say \(a_1,a_2,\dots,a_{25}\) where \(a_1\) is the top row and \(a_{25}\) is the bottom row.

Answer 2

u r told that
\[ \large a_1=5 \]
and
\[ \large a_{n}=a_{n-1}+8 \]
for \(2\leq n\leq25\)

Answer 3

for instance
\[ \large a_2=a_1+8=5+8 \]
\[ \large a_3=a_2+8=(5+8)+8=5+2\cdot 8 \]
then in general
\[ \large a_k=5+(k-1)\cdot8 \]
u should be able now to answer your questions.