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How do you calculate the sum of all numbers from 1 through 100?
The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.
What is the sequence if the sum of the first 10 terms is the same as the 58th term?
There are many sequences with this property: The sequence with every term equal to 0 has this property. In fact the sequence can be anything you like as long you make sure the 58th term is the sum of the first 10 terms. A more specific case: If you are dealing with an arithmetic sequence, i.e. a sequence of the form s(n)=a+bn for constants a and b, we can derive a relationship between a and b: s(1)+s(2)+...+s(10)=10a+55b and s(58)=a+58b From this, it follows that if s(1)+s(2)+...+s(10)=s(58), then we have 10a+55b=a+58b, which implies that 3a=b. Again, there are infinitely many sequences with this property, but if it is an arithmetic sequence, it will be of the general form s(n)=a+3an=a(3n+1)
How many even numbers are between 1 and 70?
There are 34 even numbers between 1 and 70. The even numbers in this range start from 2 and go up to 70, forming the sequence 2, 4, 6, ..., 70. This sequence can be calculated using the formula for the nth term of an arithmetic sequence, where the first term is 2, the common difference is 2, and the last term is 70. Since the sequence contains 34 terms, there are 34 even numbers in total.
How many possible sequences of four numbers are there from 1 to 8?
Question is not very clear about the context of word 'sequence' here. If I am to select 4 numbers out of four and arrange them in order then there are 4!*8C4 = 1680 different sequences possible. If the word sequence refers to some arithmetic sequence or geometric sequence, then counting is going to change for sure.
How many permutations are in the word arithmetic?
10! permutations of the word "Arithmetic" may be made.
Is this sequence arithmetic or geometric 12 48 ... 192?
It could be either. The answer depends on how many terms if any are between 48 and 192.
In an arithmetic sequence beginning with 36 and ending with 405 how many integers are divisible by 9?
41
How do you calculate the sum of all numbers from 1 through 100?
The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.
How many terms are in this sequence 3 7 11.39?
three
What is the sequence if the sum of the first 10 terms is the same as the 58th term?
There are many sequences with this property: The sequence with every term equal to 0 has this property. In fact the sequence can be anything you like as long you make sure the 58th term is the sum of the first 10 terms. A more specific case: If you are dealing with an arithmetic sequence, i.e. a sequence of the form s(n)=a+bn for constants a and b, we can derive a relationship between a and b: s(1)+s(2)+...+s(10)=10a+55b and s(58)=a+58b From this, it follows that if s(1)+s(2)+...+s(10)=s(58), then we have 10a+55b=a+58b, which implies that 3a=b. Again, there are infinitely many sequences with this property, but if it is an arithmetic sequence, it will be of the general form s(n)=a+3an=a(3n+1)
How many cuboids exist for which the volume is less than 100 cubic centimetres and the integer side lengths are in an arithmetic sequence?
476748 not ha ha
How do you find the next term of a sequence number?
The first step is to find the sequence rule. The sequence could be arithmetic. quadratic, geometric, recursively defined or any one of many special sequences. The sequence rule will give you the value of the nth term in terms of its position, n. Then simply substitute the next value of n in the rule.
How many even numbers are between 1 and 70?
There are 34 even numbers between 1 and 70. The even numbers in this range start from 2 and go up to 70, forming the sequence 2, 4, 6, ..., 70. This sequence can be calculated using the formula for the nth term of an arithmetic sequence, where the first term is 2, the common difference is 2, and the last term is 70. Since the sequence contains 34 terms, there are 34 even numbers in total.
How do you use arithmetic sequences in real life?
First we define an arithmetic sequence as one where each successive term has a common difference and that difference is constant. An example might be 1, 4, 7, 10, 13, 16, ..where the difference is 3. 1+3=4, 4+3=7 etc. Here is a common example that is given as a problem but shows a real life example of arithmetic sequences. A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern. If the theater has 20 rows of seats, how many seats are in the theater? The common difference is 8 and we want the the sum of the first 20 terms this gives us the sum of all the seats. We solve this by first finding the 20th term which is 212 and noting that the first term is 60. We add the first and the 20th terms in the sequence and multiply the sum by 20. Next we divide that product by 2. The sum we are looking for is 20(60+212)/2=2720 so there are 2720 seats in the theater! The general formula to find the sum of the first n terms in an arithmetic sequence is to multiply n by the sum of the first and nth terms in the sequence and divide that answer by 2. In symbols we write Sn=n(a1+ an)/2
How many possible sequences of four numbers are there from 1 to 8?
Question is not very clear about the context of word 'sequence' here. If I am to select 4 numbers out of four and arrange them in order then there are 4!*8C4 = 1680 different sequences possible. If the word sequence refers to some arithmetic sequence or geometric sequence, then counting is going to change for sure.
What is the pattern of 150 175 200?
The pattern in the sequence 150, 175, 200 is an arithmetic progression with a common difference of 25. Each term is obtained by adding 25 to the previous term. This can be represented by the formula for an arithmetic sequence: (a_n = a_1 + (n-1)d), where (a_n) is the nth term, (a_1) is the first term, (n) is the position of the term in the sequence, and (d) is the common difference.
How many permutations are in the word arithmetic?
10! permutations of the word "Arithmetic" may be made.
