Question

Queen Laetitia is sorting her gem collection. She starts by placing some of her

diamonds into two boxes. In every box after the first two, the Queen puts as many
diamonds as in the previous two boxes combined. If there are 30 diamonds in the
fourth box, and 128 diamonds in the seventh box, how many diamonds did
Queen Laetitia place in the tenth box?

Answer 1

Explanation:
Let's represent the missing number with "---" -- so we have so far:

--- --- --- 30 --- --- 128 --- --- ?
Now, let's say 5th position number is x and 6th position number is y
So, we have 30 + x = y and x+ y = 128
Combining these 2 equation, we get: x + 30 + x = 128 or x = 49, so y = 79

thus from 4th position, the series can be written as
30, 49, 79, 128, 207, 335, 542....
Thus, at 10th position we will have 542 !!!