Question

Typing....

Answer 1

For a given geometric sequence, the 10th term, \[a _{10}\] , is equal to \[-19\over8\] , and the 14th term, \[a _{10}\] , is equal to -38 . Find the value of the 18th term, \[a _{18}\] . If applicable, write your answer as a fraction.

Answer 2

ar^9 should be the tenth term

Answer 3

ar^13 should be 14th term

Answer 4

Ok buddy.. I'm lost already lol at^9 should be the 10th term? o_O

Answer 5

divide the 14th by 9th

Answer 6

yeah that is geometric series thats how is the sequence

Answer 7

wait check this out http://en.wikipedia.org/wiki/Geometric_series

Answer 8

Ah I erred in typing

Answer 9

a_10=-19/8 a_14=-38

Answer 10

well the nth term of any gs is ar^(n-1)

Answer 11

yeah you got that right

Answer 12

now divide the 14th by 10th

ar^13 -38 x 8
---- = r^4 = -----------
ar^9 -19

Answer 13

r^4 = 16
r = 2

Answer 14

ar^9 = -19/8

so a = -19/8 *1/512

Answer 15

Ok Ishaan, I'm going to stop you for a second and tell you, you are WAY too smart.... ok continue

Answer 16

so the 18th term is ar^17

Answer 17

thanks shark

Answer 18

You're very welcome my friend... you're just shooting this off and I'm getting lost just trying to follow >.< math is NOT my friend haha

Answer 19

substitute the value of a

i could write a as -19/8*1/r^9

so 18th term is

-19/8 *1/r^9*r^17

-19 r^(17-9)
---- x ------ = -19/8 * r^8 now put r = 2 and you will have your answer
8


math is friend just spend more time you will get way too good at it

Answer 20

So the common ratio is 2 I've gathered... that wouldn't be -2?

Answer 21

I'm sorry if my questions are dumb, this is my first time being faced with this type of problem

Answer 22

a geometric sequence is like multiplying one thing by another over and over. So if advancing from number 10 to 14 you multiply it by 16 (as is the case here) then going from 14 to 18 will be another 16, so it's 16*-38

Answer 23

no i don't think so not in gp maybe i have done some questions all with absolute values ..it is a good question

Answer 24

physopholy will correct if anything is done wrong by me he is good

Answer 25

i may get wrong values but the method is correct

Answer 26

geometric series are easy. Like 1, 2, 4, 8, 16; 1, 3, 9, 27, 81; 2, 6, 18, 54; 3, 6, 12, 24, 48..these are all different geometric series(es?). You go forward in the sequence by multiplying by whatever number. So if you find the ratio between number 8 and 6, you know the ratio between x and x-2. This is how they give you the answer: by giving you number 10 and 14. Get (#14)/(#10) and you have (#18/#14)

Answer 27

Ok.. so a_18=-608? So.. since the common ratio is 2... would it be best expressed as -1216/2? or should I just leave the answer as -608 (like I said sorry for dumb questions but this is my first time ever faced with this sort of thing >.< )

Answer 28

na just leave the answer -608/1 is also fraction

Answer 29

I see I see... ok.. I think I get it for the most part..

Answer 30

it is not dumb chris it is very good to get your doubts cleared :D continue this habit you will get better real better like zarkon

Answer 31

Thank you :) and thank you guys both so much for helping me!