Find the next three numbers in this sequence and explain the reasoning;
2/3, 2/5, 6/25, 18/125,...
Keep multiplying by 2/5
Keep multiplying by 3/5. (Sorry. Typo)
20 pints how many gallons
To find the next numbers in the sequence, we need to understand the pattern.
Looking at the numerator (the top number), we can see that it starts with 2 and doubles in each subsequent term: 2, 4, 8, 16.
Now let's focus on the denominator (bottom number). It starts with 3 and increases by 2 in every step: 3, 5, 7, 9.
Putting it together, we can determine that the overall pattern of the sequence is as follows:
2/3, 4/5, 8/7, 16/9, ...
To find the next terms, we just need to continue the pattern. The numerator should be 16 * 2 = 32, and the denominator should be 9 + 2 = 11.
Therefore, the next number in the sequence is 32/11.
If we continue the pattern one more time, the numerator will double again: 32 * 2 = 64. And the denominator will increase by 2: 11 + 2 = 13.
So, the two numbers after 32/11 are 64/13 and 128/15.