It's ON PAPER :)
in fact (2 words)
A fact is a statement that can be proven true or false based on evidence. A theory is a well-substantiated explanation of some aspect of the natural world that is supported by evidence, experimentation, and observations. The main difference is that a fact is a confirmed truth, while a theory is a broader explanation that ties together multiple facts.
I'll try to answer the question, "If the 5th term of a geometric progression is 2, then the product of its FIRST 9 terms is --?" Given the first term is A and the ratio is r, then the progression starts out... A, Ar, Ar^2, Ar^3, Ar^4, ... So the 5th term is Ar^4, which equals 2. The series continues... Ar^5, Ar^6, Ar^7, Ar^8, ... Ar^8 is the 9th term. The product P of all 9 terms is therefore: P = A * Ar * Ar^2 *...*Ar^8 Collect all the A's P = (A^9)*(1 * r * r^2 ...* r^8) P = A^9 * r^(0+1+2+...+8) There's a formula for the sum of the first n integers (n/2)(n+1), or if you don't know just add it up. 1+2+...+8 = 36 Therefore P = A^9 * r^36 Since 36 is a multiple of 9, you can simplify: P = (Ar^4)^9 Still with me? Remember that Ar^4=2 (a given fact). So finally P = 2^9 = 512. Cute problem.
AR 25-2 Ar 25-2 AR 25-2
You can get a copy of AR-25-2 from the attached link.
Let the three consecutive terms of the geometric sequence be a, ar, and ar^2. Then, we have: a + ar + ar^2 = 35 (1) a * ar * ar^2 = 1000 (2) From equation (2), we get: a^3 * r^3 = 1000 ar = 10 Substituting ar = 10 in equation (1), we get: a + 10 + 10r = 35 a + r = 25/2 Solving for a and r, we get: a = 5/2 - sqrt(65)/2 r = 5/2 + sqrt(65)/2 Therefore, the three consecutive terms of the geometric sequence are: a ≈ -7.37, ar ≈ -18.53, and ar^2 ≈ -46.34. I hope this helps! Let me know if you have any other questions.
a, ar, ar^2 and ar^3 where a and r are constants.
AR-710
19
no- these 2 words are not opposites. In fact, their meanings are really quite unrelated.
2-letter wordsaa, ar, or3-letter wordsava, avo, oar, ora, ova, var4-letter wordsarvo, vara11 words found.
[Ar] 3d10 4s2 4p6 or 2, 8, 18, 8