Create a counter pattern where the 5th term uses 18 counters
a+4d = 18
so, one way would be 2,6,10,14,18
To create a counter pattern where the 5th term uses 18 counters, we can start by determining the pattern for each term.
Let's assume the first term starts with 1 counter.
First term: 1 counter
Second term: 2 counters
Third term: 3 counters
Fourth term: 4 counters
Fifth term: 18 counters
From the given information, we can see that the increment between each term is increasing by 1, except for the fifth term.
To find the increment for the fifth term, we can subtract the fourth term from the fifth term:
18 counters - 4 counters = 14 counters
Therefore, the increment for the fifth term is 14 counters.
Now, we can calculate the second, third, and fourth terms using the pattern we observed:
Second term = First term + increment
= 1 counter + 1 counter
= 2 counters
Third term = Second term + increment
= 2 counters + 1 counter
= 3 counters
Fourth term = Third term + increment
= 3 counters + 1 counter
= 4 counters
Hence, the counter pattern where the 5th term uses 18 counters is:
1 counter, 2 counters, 3 counters, 4 counters, 18 counters.
To create a counter pattern where the 5th term uses 18 counters, we need to establish the pattern. Let's break it down step by step:
1st term: We start with 0 counters.
2nd term: We add a certain number of counters.
3rd term: We add the same number of counters as the 2nd term.
4th term: We add the same number of counters as the 2nd and 3rd terms combined.
5th term: We need to determine how many counters we need to reach 18.
To find the pattern, let's observe the differences between consecutive terms:
2nd term - 1st term = (unknown number of counters)
3rd term - 2nd term = (same unknown number of counters)
4th term - 3rd term = 2*(unknown number of counters)
Now, to determine the unknown number of counters needed, we can use a system of equations:
Let the unknown number of counters be represented by 'x'.
2nd term - 1st term = x
3rd term - 2nd term = x
4th term - 3rd term = 2x
Simplifying the equations:
x = (unknown)
x = (unknown)
2x = (unknown)
Since all three expressions are equal, we can equate them:
x = 2x
Solving for x:
x = 0
Oops! It seems we made an error while working with the equations. Let's try again.
Let's redefine the terms:
2nd term: We add 'x' counters.
3rd term: We add 'x' counters.
4th term: We add '2x' counters.
5th term: We need to find the number of counters that makes the total 18.
Now, let's repeat the steps:
2nd term - 1st term = x
3rd term - 2nd term = x
4th term - 3rd term = 2x
5th term - 4th term = 18
Using the equations:
x = (unknown)
x = (unknown)
2x = (unknown)
18 - 2x = (unknown)
Let's equate the expressions:
x = x
x = x
2x = 18 - 2x
Now, we can solve the equation:
2x + 2x = 18
4x = 18
x = 18/4
x = 4.5
Since we cannot have a fraction of counters, we will need to adjust the pattern. Instead of adding 4.5 counters, we can add either 4 or 5 counters to each term.
So, here is the adjusted pattern:
1st term: 0 counters
2nd term: Add 4 counters (total 4 counters)
3rd term: Add 4 counters (total 8 counters)
4th term: Add 8 counters (total 16 counters)
5th term: Add 2 counters (total 18 counters)
In this pattern, the 5th term uses 18 counters.