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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.
