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What is the 32nd term of the arithmetic sequence where a1 equals 15 and a13 equals -57?
Suppose the sequence is defined by an = a0 + n*d Then a1 = a0 + d = 15 and a13 = a0 + 13d = -57 Subtracting the first from the second: 12d = -72 so that d = -6 and then a0 - 6 = 15 gives a0 = 21 So a32 = 21 - 32*6 = -171
Equations that have the same solution?
It is not clear what the question requires. Yes, there are plenty of equations that have the same solution. For example, each and every equation of direct proportionality has the solution (0, 0). So what? every polynomial of the form y = anxn + an-1xn-1 + ... + a1x + a0 has the solution (0, a0). Again, so what?
Prove if a number is divisible by 3 then the sum of its digits must also be divisible by 3?
Suppose an (n+1)-digit number, X, is divisible by 3. Let X = a0*100 + a1*101 + a2*102 + ... + an*10n = a0 + a1*(1+9) + a2*(1+99) + ... + an*(1+999..9) = [a0 + a1 + a2 + ... + an] + [a1*9 + a2*99 + ... + an*999..9] 3 divides 9, 99, 999, etc so 3 divides each term in the second brackets (parentheses). Therefore 3 must divide the sum in the first brackets. That is, 3 must divide the sum of digits.
What is 7a to the 0 power?
Anything (except zero) to the power of zero is 1. If written as 7a0, this is operated as 7 x (a0) = 7 x 1 = 7. If written as (7a)0, it is simply 1 by the first statement.
What size is an A0?
83.0 x 115.4 cm / 32.7 x 45.4 inches
