24 cats line up for breakfast. the first cat eats one fish, the second cat eats two fish, and so on, with each cat eating one more fish than the one before it. How many fish are eaten in total?
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To find the total number of fish eaten, we need to find the sum of the fish eaten by each cat.
The pattern here is that each cat eats one more fish than the one before it. We can express this pattern using arithmetic progression. The formula to find the sum of an arithmetic progression is:
Sn = n/2 * (a + l)
where Sn is the sum of the progression, n is the total number of terms, a is the first term, and l is the last term.
In this case, we have the following information:
n = 24 (24 cats)
a = 1 (the first cat eats one fish)
l = 24 (the last cat eats 24 fish)
Using the formula, we can calculate the sum:
Sn = 24/2 * (1 + 24)
= 12 * 25
= 300
Therefore, in total, the cats will eat 300 fish.