For a given geometric sequence, the 5th term, a[5] , is equal to 11/16 , and the 8th term, a[8] , is equal to 44 . Find the value of the 11th term, a[11] . If applicable, write your answer as a fraction.

Question

For a given geometric sequence, the 5th term, a[5] , is equal to   11/16 , and the 8th term, a[8]  , is equal to 44  . Find the value of the 11th term, a[11]  . If applicable, write your answer as a fraction.

anonymous · Answer

Please help quickly!!!

anonymous · Answer

this is not exactly on point but its close. 5459/50 or 109.18.

campbell_st · Answer

well a term in a geometric sequence is 

$$a_{n} = a_{1} \times r^{n -1}$$

so find the common difference 

$$\frac{11}{16} = a_{1} \times r^{5-1}$$

and 

$$44 = a_{1} \times r^{8-1}$$

rewriting the equation gives 

$$44 = a_{1} \times r^4 \times r^3$$

now subtituting the 5th term 

$$44 = \frac{11}{16} \times r^3$$

then 

$$64 = r^3$$

so the common ratio is r = 4

since you know the 8th term the 11th term will be 

$$a_{11} = a_{1} \times r^{11 -1}....or.... a_{1} \times r^{10}$$
rewriting in terms of the 8th term 

$$a_{11} = a_{1} \times r^3 \times r^3$$

so 

$$a_{11} = 44 \times 4^3$$

or 

$$a_{11} = 44 \times 64$$

anonymous · Answer

that ain't right.

anonymous · Answer

oh wait. I was adding.

campbell_st · Answer

ok well have a look at this 

5th term 11/16

6th term  11/16 x 4 = 11/4

7th term 11/4 x 4 = 11

8th term  11 x 4 = 44

funny I seem to have the common ratio correct... 

9th term 

44 x 4 = 176

10th term    

176 x 4 = 704

11th term 

704 x 4 = 2816

perhaps you could post your solution...it would make interesting reading...