A boy decided to cut 10 pieces of wood from a length of wood so that the first piece was 5cm the second 10cm, the third 15cm, the fourth 20cm and so on until he had cut 10 pieces, each one 5cm longer than the one he had cut before. What length of the wood did he use
To find the total length of wood the boy used, we need to add up the lengths of all 10 pieces of wood.
The first piece was 5cm long.
The second piece was 10cm long, which is 5cm longer than the first piece.
The third piece was 15cm long, which is 5cm longer than the second piece.
Continuing this pattern, the fourth piece was 20cm long (15cm + 5cm), the fifth piece was 25cm long (20cm + 5cm), and so on.
Therefore, the length of each piece can be represented by the arithmetic sequence: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
To find the total length of wood used, we need to add up all the lengths:
5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 = 275.
Therefore, the boy used a length of wood that was 275cm long.
To find the total length of the wood used, we need to calculate the sum of the lengths of the 10 pieces. Since each piece is 5cm longer than the previous one, we can use an arithmetic sequence formula to find the length of the final piece.
The formula for finding the nth term of an arithmetic sequence is given by:
an = a + (n - 1)d
Where:
an is the nth term,
a is the first term,
n is the number of terms, and
d is the common difference between terms.
Given that the first piece is 5cm, the common difference between the pieces is 5cm, and there are 10 pieces, we can substitute these values into the formula:
a = 5cm
d = 5cm
n = 10
an = 5cm + (10 - 1)5cm
an = 5cm + 9 * 5cm
an = 5cm + 45cm
an = 50cm
Therefore, the length of the final piece is 50cm. To find the total length, we need to sum the lengths of all the pieces:
total length = 5cm + 10cm + 15cm + ... + 50cm
To calculate the sum of an arithmetic sequence, we can use the following formula:
sum = (n/2)(a + an)
Substituting the values:
n = 10
a = 5cm
an = 50cm
sum = (10/2)(5cm + 50cm)
sum = 5 * 55cm
sum = 275cm
Therefore, the boy used a length of wood measuring 275cm.
To find out the length of the wood the boy used, we need to determine the total length of all the 10 pieces he cut.
We know that the length of each piece is 5cm longer than the previous one. Thus, we can create a pattern:
1st piece: 5 cm
2nd piece: 5 cm + 5 cm = 10 cm
3rd piece: 10 cm + 5 cm = 15 cm
4th piece: 15 cm + 5 cm = 20 cm
And so on...
From the pattern, we can see that each piece is increasing by 5 cm. This implies that the length of the nth piece can be calculated using the formula:
Length of nth piece = Length of (n-1)th piece + 5 cm
Using this formula, we can find the length of each piece in the pattern:
1st piece: 5 cm
2nd piece: 5 cm + 5 cm = 10 cm
3rd piece: 10 cm + 5 cm = 15 cm
4th piece: 15 cm + 5 cm = 20 cm
5th piece: 20 cm + 5 cm = 25 cm
6th piece: 25 cm + 5 cm = 30 cm
7th piece: 30 cm + 5 cm = 35 cm
8th piece: 35 cm + 5 cm = 40 cm
9th piece: 40 cm + 5 cm = 45 cm
10th piece: 45 cm + 5 cm = 50 cm
To find the total length of the wood, we simply add up the lengths of all the pieces:
Total length = 5 cm + 10 cm + 15 cm + 20 cm + 25 cm + 30 cm + 35 cm + 40 cm + 45 cm + 50 cm
Total length = 275 cm
Therefore, the boy used a length of wood that was 275 cm long.