Question

sum decimals
find a pattern
and then
complete
the figure.
.01
.02 .02
.03 .04 .03
.04 .07 .07 .04
.05 .14 .11
.16
.22
.91 .08
1.54
.10 3.36
if this continued,
what would be the
first number in the
20th row?
what would be
the first number
in the 101st row?

Explanation:

Step1: Identify the pattern for first numbers

Looking at the first numbers of each row:

• Row 1: \(0.01\)
• Row 2: \(0.02\)
• Row 3: \(0.03\)
• Row 4: \(0.04\)
• Row 5: \(0.05\)

We can see that the first number in the \(n\)-th row is \(0.01\times n\).

Step2: Find the first number in the 20th row

Using the pattern \(a_n = 0.01\times n\), where \(n = 20\).
\(a_{20}=0.01\times20 = 0.20\)

Step3: Find the first number in the 101st row

Using the same pattern \(a_n = 0.01\times n\), where \(n = 101\).
\(a_{101}=0.01\times101 = 1.01\)

Answer:

First number in the 20th row: \(0.20\)
First number in the 101st row: \(1.01\)