12. Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 8 and the 8th term is 18.
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By combining the equations we can found that the number of impulse clothing and Opal essence stores by equations be C (3x+5)/2 where x is the number of years after the brand's founding.
Given The equation showing number of impulse clothing stores is C=2x. The equation showing number of clothing stores be C=x+5.
We have to first plot both the equations on the graph.
For plotting we need points which can be calculated as
C=2x
when x=1 ,C or y=2
when x=3 , C or y=6
C=x+5
when x=0 ,C or y=5
when x=1 ,C or y=6
By combining both equations we get
C=(3x+5)/2
Plot this also and finding points
when x=0 , C=5/2
when x=1 , C=4
Hence the combination of both statements which shows the total stores owned is C=(3x+5)/2
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Given:
The sequence is -8, -12, -16.
To find:
The nth and 52th term of the given sequence.
Solution:
We have,
-8, -12, -16
It is an AP because the difference between consecutive terms are equal. Here, first term is -8 and the common difference is
The nth term of an AP is
Where, a is first term and d is common difference.
Putting a=-8 and d=-4, we get
Putting n=52, we get
Therefore, the equation for the nth term of the given sequence is and the 52nd term of the sequence is -212.