Question

1. A list of 8 numbers is formed such that each new number in the list is the product of the two previous numbers. Find the first number if the last three are shown: 2. What number is directly above 140 in this array of numbers? The pics are attached Have a great day! <3

Answer 1

1. 1/4 4 1 4 4 16 64 1024

2. 118

Explanation:

1. 16 is obtained as 1024/64 = 16

before 16 goes: 64/16 = 4

before 4 goes: 16/4 = 4

before the second 4 goes: 4/4 = 1

before 1 goes: 4/1 = 4

before the third 4 goes: 1/4

2. From row 1 to row k, there are k² numbers (notice that rows finished in 1, 4, 9, etc., all perfect squares). 12² = 144, so 140 is on 12th row.

A number in row k is 2k less than the number directly below it. For example, 3 is on 2nd row, then is 2*2 = 4 units less than the number directly below it, which is 7.

The number above 140 is on the 11th row, then above 140 is 140 - 2*11 = 118.