John has a collection of mixed number sequences. He starts with 2 and adds 1/3 to it to get the next number in the sequence. Then, he adds 1/2 to the second number to get the third number in the sequence. If this pattern continues, what is the fifth number in the sequence?

Answer 1

To find each number in the sequence, John adds a fraction to the previous number. The fractions he adds are 1/3, 1/2, 2/5, and 3/7. We can see a pattern: the numerator of each fraction is counting up by 1, while the denominator is counting down by 1.

The fifth number in the sequence is found by adding 3/7 to the fourth number. The fourth number is 2 + 1/3 + 1/2 + 2/5 = 2 + 10/30 + 15/30 + 12/30 = (2 + 10 + 15 + 12)/30 = 39/30 = 13/10.

Adding 3/7 to 13/10, we get (13/10) + (3/7) = (91/70) + (30/70) = 121/70.

Therefore, the fifth number in the sequence is 121/70.