aaron is skipping stones across a pond.(A "skip"is a short bounce in the water.)The first stone skips 1 time, the second skips 2 times, the third stone skips 4 times,and the fourth stone skips 8 times.
if this patten continues,how many total skips will the 10th stone make? how many total skips will have been made?
what is the patten?if yo knew the number of the stone,such as 11th,or n,how would you figure out how many skips it would take?
To determine the pattern for the number of skips made by each stone, we can observe that each stone seems to double the number of skips compared to the previous one. The first stone skips 1 time, the second stone skips 2 times (1 x 2), the third stone skips 4 times (2 x 2), and the fourth stone skips 8 times (4 x 2).
So, it can be inferred that for each stone, the number of skips can be calculated by multiplying the number of skips of the previous stone by 2.
Now, to find the number of skips made by the 10th stone, we can apply this pattern. By multiplying the number of skips of the 9th stone (which would be 512) by 2, we get 1024. Therefore, the 10th stone would make a total of 1024 skips.
To find the total number of skips that have been made, we can sum up the number of skips for each stone from the first to the 10th.
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1023
Therefore, a total of 1023 skips would have been made by the 10 stones.
To find the number of skips for any given stone, such as the 11th or the nth stone, you can use the formula: 2^(n-1), where n represents the number of the stone. For example, for the 11th stone, you would substitute n with 11 in the formula:
2^(11-1) = 2^10 = 1024
Hence, the 11th stone would make a total of 1024 skips.