Row 1 1 row2 3 5 row 3 7 9 11 row 4 13 15 17 row 5 21 23 25 27 29 Find the middle number in the 99th row What is the sum of the numbers in the 30th row?

Answer 1

First, you didn't enter the numbers correctly...

Row 1: 1

Row 2: 3, 5

Row 3: 7, 9, 11

Row 4: 13, 15, 17, 19 (you were missing the 19)

Row 5: 21, 23, 25, 27, 29

To get an idea of the answer to the first question, continue the pattern a couple more rows, focusing on the middle number(s)...

Row 1: 1

Row 2: 3, 5

Row 3: 7, 9, 11

Row 4: 13, 15, 17, 19

Row 5: 21, 23, 25, 27, 29

Row 6: 31, 33, 35, 37, 39, 41

Row 7: 43, 45, 47, 49, 51, 53, 55

If you've studied median, you know it's the middle number when the data is arranged in order, and that if there are two "middle" numbers, the median is the mean of the two numbers (i.e. median of row 4 is (15 + 17)/2 = 16).

Median of

Row 1 is 1

Row 2 is 4

Row 3 is 9

Row 4 is 16

Row 5 is 25

Row 6 is 36

Row 7 is 49

The median of each row is the square of the row number (i.e. row 6... 6^2 = 6*6 = 36)

So you can infer that the median (middle number) in the 99th row would be 99 squared, which is 9801.

For the second part of the question, examine the sums of the numbers in each row...

Row 1: 1 Sum = 1

Row 2: 3, 5 Sum = 8

Row 3: 7, 9, 11 Sum = 27

Row 4: 13, 15, 17, 19 Sum = 64

Row 5: 21, 23, 25, 27, 29 Sum = 125

The pattern to recognize here is that the sum of the numbers in each row is the cube of the row number (i.e. Row 3... 3^3 = 3*3*3 = 27)

So you can infer that the sum of the numbers in the 30th row is 30 cubed, which is 27,000.