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?
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.