Francis has been tweeting about missing farm animals and missing children. He has been tweeting more frequently in the last few weeks. Two weeks ago, Francis sent 18 tweets about missing farm animals and 2 tweets about missing children; last week, he sent 22 tweets about farm animals and 3 tweets about children; this week, he sent 26 tweets about farm animals and 4 about missing children. If this pattern continues, how many more tweets about farm animals than tweets about missing children will Francis send in the next 52 weeks?
+23254 For the children: the pattern is 2, 3, 4, ... (adding 1 each time)
For the animals: the pattern is 18, 22, 26, ... (adding 4 each time)
These are both arithmetic sequences because each increase by adding the same amount each time.
I will answer these by using formulas from the mathematical area of arithmetic sequences and series. If you are not familiar with these, they can be done without the formulas, but it will take longer. Post back if you want the more basic way.
The nth term of an arithmetic sequaen can be found by the formul: tn = t1 + (n-1)d where: tn is the nth term (or last term) t1 is the first term n is the number of terms d is the common difference
To solve this problem we are starting with the first new terms in the sequences (5 for children and 30 for animals)
For children, the first term will be 5, the number of terms is 52, and the common difference is 1.
Putting these into the equation, we get: tn = 5 + 51(1) = 56
For animals, the first term will be 30, the number of terms is 52, and the common difference is 4.
Putting these into the equation, we get: tn = 30 + 51(4) = 234
If I read the problem correctly, I will need to know the total number of tweets more for animals than for children; so if I find the total number of tweets for animals and subtract the total number of tweets for children, I will have the answer.
For arithmetic series, the sum has this formula: S = n(f + l) / 2 where S is the sum n is the number of terms f is the first term and l is the last term.
For children, n = 52, f = 5, and l = 56.
Putting these into the equation, we get: S = 52(5 + 56) / 2 = 1716 total tweets for children.
For animals, n = 52, f =30, and l = 234.
Putting these into the equation, we get: S = 52(30 + 234)/2 = 6864 total tweets for animals.
The difference is 6864 - 1716 = 5148.
+23254 For the children: the pattern is 2, 3, 4, ... (adding 1 each time)
For the animals: the pattern is 18, 22, 26, ... (adding 4 each time)
These are both arithmetic sequences because each increase by adding the same amount each time.
I will answer these by using formulas from the mathematical area of arithmetic sequences and series. If you are not familiar with these, they can be done without the formulas, but it will take longer. Post back if you want the more basic way.
The nth term of an arithmetic sequaen can be found by the formul: tn = t1 + (n-1)d where: tn is the nth term (or last term) t1 is the first term n is the number of terms d is the common difference
To solve this problem we are starting with the first new terms in the sequences (5 for children and 30 for animals)
For children, the first term will be 5, the number of terms is 52, and the common difference is 1.
Putting these into the equation, we get: tn = 5 + 51(1) = 56
For animals, the first term will be 30, the number of terms is 52, and the common difference is 4.
Putting these into the equation, we get: tn = 30 + 51(4) = 234
If I read the problem correctly, I will need to know the total number of tweets more for animals than for children; so if I find the total number of tweets for animals and subtract the total number of tweets for children, I will have the answer.
For arithmetic series, the sum has this formula: S = n(f + l) / 2 where S is the sum n is the number of terms f is the first term and l is the last term.
For children, n = 52, f = 5, and l = 56.
Putting these into the equation, we get: S = 52(5 + 56) / 2 = 1716 total tweets for children.
For animals, n = 52, f =30, and l = 234.
Putting these into the equation, we get: S = 52(30 + 234)/2 = 6864 total tweets for animals.
The difference is 6864 - 1716 = 5148.
