SOLUTION: The sixth term of a geometric series of positive terms is 10 and the sixteenth term is 0.1, what is the eleventh term?

Algebra.Com
Question 1078683: The sixth term of a geometric series of positive terms
is 10 and the sixteenth term is 0.1, what is the eleventh term?

Found 2 solutions by akch2002, Edwin McCravy:
Answer by akch2002(12)   (Show Source): You can put this solution on YOUR website!
We have Tn = a*r^(n-1) where Tn is nth tern, a = 1st term and r = common ratio.
Here 10 = a*r^(6-1)= ar^5 ----(1)
Also 0.1 = a*r^(16-1) = a r^15 ----- (2)
(1)/(2) gives r= 0.01^0.1
and, hence, a = 10/(0.01)^0.5
Hence, 11th term = T11 = ar^10= [10/0.01^0.5]*0.01
= 10(0.01)^0.5
= 1
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Here's a different approach:

The sixth term of a geometric series of positive terms
is 10 and the sixteenth term is 0.1, what is the eleventh term? 


Then the series is:



Each term is the preceding term multiplied by the 
common ratio r, so



So we have this system of equations:



We solve the first equation for r5:




We substitute for r5 in the second equation:







Multiply both sides by 10



So





But since we are told the terms are all positive,



and the eleventh term is 1.

Edwin
RELATED QUESTIONS

the sixth term of a geometric series of positive number is 10 and the sixteenth term is... (answered by Boreal)
The seventh term of arithmetic progression series is 29 and the eleventh term is 54.... (answered by rothauserc)
What is the sixth term of the geometric sequence whose third term is 16 and eighth term... (answered by stanbon)
the third term of a geometric sequence is 4 and the sixth term is 32/27. find the nth... (answered by MathLover1)
The 2nd term of a geometric series is 80 and the sixth term is 16/125. Find the common... (answered by Cromlix)
Find the indicated terms of the geometric sequence with the given description. The... (answered by josgarithmetic)
The first term of a geometric series are 1,x,y, and the first three terms of an... (answered by josgarithmetic)
the sum of second term and 3rd terms of geometric sequences is 280 and sum of fifth and... (answered by ikleyn)
What is the common ratio of the third term of a geometric progression is 360 the sixth... (answered by amoresroy)