A snail is crawling up the side of a wall that is 3 meters high. Each day, he crawls up 40cm. The first night, he slips back down 2cm; the second night he slips down 4cm; the third night he slips down 6cm; and so on at the same rate.(He was getting more tired each night!) How many days did it take the snail to reach the top of the wall?

Pls help me!!

It took 6.

Target: 3 meters or 300 cm

First day: 0 + 40 - 2 = 38
Second day: 38 + 40 - 4 = 74
Third day: 74 + 40 - 6 = 108
Fourth day: 108 + 40 - 8 = 140
Fifth day: 140 + 40 - 10 = 170
Sixth day: 170 + 40 - 12 = 198
Seventh day: 198 + 40 - 14 = 224
Eighth day: 224 + 40 - 16 = 248
Ninth day: 248 + 40 - 18 = 270
Tenth day: 270 + 40 = 310 cm (he didn't slip because he already reached the top)

Thus it took him 10 days.
hop this helps~ `u`

Thanks jai !! So much

To solve this problem, we need to determine how many days it will take for the snail to reach the top of the wall.

Let's break down the information we have:
- The snail climbs 40cm up the wall during the day.
- Each night, the snail slips down a certain number of centimeters, increasing by 2cm each night.

To find the number of days it takes the snail to reach the top of the wall, we can calculate the total progress made by the snail each day.

On the first day, the snail climbs 40cm, and then slips down 2cm at night. So the net progress made on the first day is 40cm - 2cm = 38cm.

On the second day, the snail climbs another 40cm, and then slips down 4cm at night. So the net progress made on the second day is again 40cm - 4cm = 36cm.

Following this pattern, we can deduce that the net progress made each day decreases by 2cm. Therefore, the net progress made on the third day is 34cm, on the fourth day is 32cm, and so on.

To calculate the number of days it takes for the snail to reach the top of the wall, we can set up the following equation:

Total progress made = 38cm + 36cm + 34cm + ... + (2cm less each day)

We can simplify this equation using the arithmetic series formula:

n/2 * (first term + last term) = Total progress made

Here, n represents the number of days it takes for the snail to reach the top of the wall, and the first term is 38cm, and the last term is 2cm.

Plugging these values in, we get:

n/2 * (38cm + 2cm) = Total progress made

Simplifying further:

n/2 * 40cm = Total progress made

Therefore, to solve for n, we need to know the total progress made by the snail.

The total progress made by the snail can be calculated by finding the sum of an arithmetic sequence, where the first term is 38cm, the common difference is -2cm (due to the snail slipping back each night), and the last term is 2cm.

To find the number of terms in this sequence, we can use the following formula:

Number of terms = (last term - first term) / common difference + 1

Plugging in the values, we get:

Number of terms = (2cm - 38cm) / (-2cm) + 1

Simplifying further:

Number of terms = (-36cm) / (-2cm) + 1

Number of terms = 18 + 1

Number of terms = 19

Therefore, the total progress made by the snail is the sum of an arithmetic sequence with 19 terms.

Now we can solve for n using the formula we derived earlier:

n/2 * 40cm = Total progress made

n/2 * 40cm = (38cm + 36cm + 34cm + ... + 2cm)

Substituting the number of terms (19) and solving for n:

n/2 * 40cm = 19/2 * (38cm + 2cm)

n/2 * 40cm = 19/2 * 40cm

Simplifying further:

n = 19/2

n = 9.5

Since the number of days must be a whole number, we round up to the next integer:

n = 10

Therefore, it takes the snail 10 days to reach the top of the wall.