The first term in a certain geometric sequence is X and the fourth term in the sequence is 27X, where X is a nonzero number. Which is the tenth term?
Can you please let me know of formulas that I can use for future references. Thanks a lot!
2006-10-18 04:01:25 · 4 answers · asked by Nif 2 in Science & Mathematics ➔ Mathematics
People are asking all sorts of Math Questions to cheat the system. Have you learnt anything about the sequences. If you did it should be easy to do this . What I can see is that the X is there to just confuse you. Whether it is the 10th term or 100th term the answer would be Mx where M is the numerical factor having no X. So can you now figure out the 10th term. I can. each of the successive terms get multiplied by three (cube root of 27 (there are three terms after the first). So the tenth term would be 3*9X. 9 is 10-1. There are no hard fast equations to solve sequences of this sort.
2006-10-18 04:13:47 · answer #1 · answered by Anonymous · 0⤊ 0⤋
In a gemetric series, a_m = a_n*(r^(m-n)) if m > n. In this case, a_1 = x and a_4 = 27x, meaning m = 4 and n = 1, so we have 27x = x*(r^3), and r = 3 from simple algebra. Now, find a_10 = a_1*3^9, using a new m = 10. So a_10 is x times three to the ninth power, a large number that you should be able to find using a standard calculator.
2006-10-18 04:05:50 · answer #2 · answered by DavidK93 7 · 1⤊ 0⤋
a4 = 5 = 4d + c Sum of first 6 words = 3(a1 + a6) = 10 => a1 + a6 = 10/3 = d + c + 6d + c = 7d + 2c -8d + 7d = -10 + 10/3 => -d = -20/3 => d = 20/3 c = 5 - 80/3 = -sixty 5/3 Sum of first 19 words = 19/2 * (-15 + a hundred and five) = 855
2016-12-16 09:42:49 · answer #3 · answered by Anonymous · 0⤊ 0⤋
19683
3^9
looks like 1 3 9 27 ................ 19683
2006-10-18 04:09:43 · answer #4 · answered by bob h 3 · 1⤊ 0⤋