Question 6

1st row : 3 numbers = 1 + 2 = 1 + 2 × 1
2nd row : 5 numbers = 1 + 4 = 1 + 2 × 2
3rd row : 7 numbers = 1 + 6 = 1 + 2 × 3
...
...
80th row : 1 + 2 × 80 = 1 + 160 = 161 numbers

How many numbers are there altogether?

Pairing method:

1st row + 80th row : 3 + 161 = 164
2nd row + 79th row : 5 + 159 = 164
3rd row + 78th row : 7 + 157 = 164

(Each row pair has a total of 164 numbers)

Number of row pairs = 80 ÷ 2 = 40

Total number of numbers = 40 × 164 = 6560


The last number in row 80 is 6560.

Question 5

Odd numbered group → odd numbers
Even numbered group → even numbers

100th group →100 is even → 100 even numbers in that group.


Trick is to look at the biggest number of each group first.

Last of 1st group = 1 = 1 × 1
(It is also the first in the group since there is only 1 number).

Last of 2nd group = 4 = 2 × 2
Last of 3rd group = 9 = 3 × 3
Last of 4th group = 16 = 4 × 4
Last of 5th group = 25 = 5 × 5
...
Last of 99th group = 99 × 99 = 9801

To get to the smallest number of the next group, just add 1.

9801 + 1 = 9802 (answer)

Alternatively,

biggest number in the 100th group = 100 × 100 = 10000

There are 100 even numbers in the 100th group.

To get to the smallest number in the group, subtract 99 times of 2.

(This is basically going backwards 99 times)

10000 - 99 × 2 = 10000 - 198 = 9802 (same answer as the other method)

Thank you J .