Randy had a sheep that started eating more and more as each day passed. On July 1,

Randy’s sheep ate 5 carrots. On July 2, Randy’s sheep ate 11 carrots. On July 3, the sheep ate 18 carrots. How many carrots will the hungry sheep eat on July 30th?

Looks like you're one day off. On July 1 the sheep ate 5 carrots.

on July nth, the sheep eats n(n+9)/2 carrots.

On July 30, that's 30(39)/2 = 15*39 = 585 carrots

July 2: 5

July 3: 11
July 4: 18
July 5: 26
July 6: 35
July 7: 45
July n: 5 + 6 +.. + (n+3)
= 4(n-1) + 1 + 2 +...+ (n-1)
= 4(n-1) + (n-1)n/2
July 30 = 4*29 + 30*29/2 = 551

To find out how many carrots the sheep will eat on July 30th, we need to find the pattern in the numbers given. It looks like the amount of carrots the sheep eats each day is increasing by a certain number.

If we observe the pattern carefully, we can see that the number of carrots the sheep eats each day is increasing by 6 each time:

July 1: 5 carrots
July 2: 5 + 6 = 11 carrots
July 3: 11 + 6 = 18 carrots

So, on July 30th, we can find the number of carrots using the pattern:

Number of days from July 3rd to July 30th = 30 - 3 = 27 days

Number of carrots eaten on July 30th = 18 + (27 * 6) = 18 + 162 = 180 carrots

Therefore, the hungry sheep will eat 180 carrots on July 30th.