5
10,11,12,13,14 or 8,10,12,14,16
Suppose the first term is a, the second is a+r and the nth is a+(n-1)r. Then the sum of the first five = 5a + 10r = 85 and the sum of the first six = 6a + 15r = 123 Solving these simultaneous equations, a = 3 and r = 7 So the first four terms are: 3, 10, 17 and 24
5
x is the first term and d is the difference then x + 3d = 15 and sum of first five terms isx + (x+d) + (x+2d) + (x+3d) + (x+4d)so 5x + 10d = 55 ie x + 2d = 11As x + 3d = 15, d = 4 and x = 3,giving the five terms as 3, 7, 11, 15 and 19
If that is + 192 then divide all terms by 3 and it is (x+8)(x+8) when factored
Vienna, Austria is located at 48N 16E.
All but John Adams served two terms. The total of the first five was nine terms or 36 years (almost - Washington's first term was about an month short.)
48N and 2E coordinates correspond to Paris, the capital city of France.
Yes, here's the proof. Let's start out with the basic inequality 36 < 48 < 49. Now, we'll take the square root of this inequality: 6 < √48 < 7. If you subtract all numbers by 6, you get: 0 < √48 - 6 < 1. If √48 is rational, then it can be expressed as a fraction of two integers, m/n. This next part is the only remotely tricky part of this proof, so pay attention. We're going to assume that m/n is in its most reduced form; i.e., that the value for n is the smallest it can be and still be able to represent √48. Therefore, √48n must be an integer, and n must be the smallest multiple of √48 to make this true. If you don't understand this part, read it again, because this is the heart of the proof. Now, we're going to multiply √48n by (√48 - 6). This gives 48n - 6√48n. Well, 48n is an integer, and, as we explained above, √48n is also an integer, so 6√48n is an integer too; therefore, 48n - 6√48n is an integer as well. We're going to rearrange this expression to (√48n - 6n)√48 and then set the term (√48n - 6n) equal to p, for simplicity. This gives us the expression √48p, which is equal to 48n - 6√48n, and is an integer. Remember, from above, that 0 < √48 - 6 < 1. If we multiply this inequality by n, we get 0 < √48n - 6n < n, or, from what we defined above, 0 < p < n. This means that p < n and thus √48p < √48n. We've already determined that both √48p and √48n are integers, but recall that we said n was the smallest multiple of √48 to yield an integer value. Thus, √48p < √48n is a contradiction; therefore √48 can't be rational and so must be irrational. Q.E.D.
7
The coordinates 48N 4E correspond to the city of Lyon in France. Lyon is known for its historical architecture, vibrant food scene, and proximity to the French Alps.
2,1,0 is th sequence of its terms
Paris, France
5
no clue
What does N equal? Well to solve the problem you would do N+7x1, N+7x2, N+7x 3, N+7x4, N+7x5 to figure out the first five terms.