How do I find the sixth term of a geometric sequence for which t_5 = 24 and t_8 = 3?

Alfred Elliott

Alfred Elliott

Answered question

2023-03-23

How do I find the sixth term of a geometric sequence for which t 5 = 24 and t 8 = 3 ?

Answer & Explanation

inconcusovg9s

inconcusovg9s

Beginner2023-03-24Added 6 answers

t 8 < t 5 so Thus reducing. This indicates that the ratio is below one.
Let k be a constant
Let the ratio be 1 r
giving:
t 5 = k ( 1 r ) 5 = 24 ........................( 1 )
t 8 = k ( 1 r ) 8 = 3 .............................( 2 )
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To find 1 r divide equation 1 by equation 2 giving
( 1 r ) 5 - 8 = 24 3 = 8
( 1 r ) - 3 = 8
r 3 = 8
r = 2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To find k
Substitute for r in equation ( 1 ) giving
k ( 1 2 ) 5 = 24
k = ( 2 5 ) ( 24 )
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We can now respond to the question:
t 6 = ( 2 5 ) ( 24 ) ( 1 2 ) 6 "" Again, I will let you work that out.""
By the way: 2 5 × 1 2 6 = 2 5 2 6 = 1 2
So 1 2 × 12

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