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A frog fell into a 30-meter-deep dry well, climbing 3 meters every day and dropping 1 meter at night. He asked the frog if he could come out of the well in a few days.
A frog falls into a 30-meter-deep dry well, climbs 3 meters every day, drops 1 meter at night, and the frog can get out of the well in 27 days.

1. Snails reach a new height every day, so it is necessary to calculate the height during the day;

2. The height of the first day is 3 meters; The height of the second day is 3+(3-2) ×1= 4m; The height of the third day is 3+(3-2) × 2 = 5m, in which a series of numbers, 3, 4, 5, 6 ..., can be calculated.

3. The general rule of this series is: the maximum height during the day on the nth day is 3+(3-2) × n = 3+n;

4. A 30-meter-deep dry well, that is, when 3+n=30, calculates that n=27 days, that is, it takes 27 days for the snail to climb out of the wellhead.

Extended data:

Every number in a series is called an item in this series. The number ranked first is called 1 item of this series (usually also called the first item), the number ranked second is called the second item of this series, and so on, and the number ranked n is called the n item of this series, usually represented by an.

In a series, if the sum of each term and the following term is the same constant, then this series is called equal sum series, and this constant is called the sum of series.

For a sequence, if the sum of any continuous k(k≥2) terms is equal, we call it an equal sum sequence, and its property is that it must be a cyclic sequence.