Term of the arithmetic sequence 12, 10, 8
1 answer:
You might be interested in
Given:
The sequence is:
To find:
The 6th term of the given sequence.
Solution:
We have,
Here, the first term is:
The ratio between consecutive terms are:
The given sequence has a common ratio 5. So, the given sequence is a geometric sequence.
The nth term of a geometric sequence is:
Where, a is the first term and r is the common ratio.
Substitute to get the 6th term.
Therefore, the 6th term of the given sequence is 50000.
Correct so far. Finish up.
.. (x +3)(x)(x -1) = 1170
.. x^3 +2x^2 -3x -1170 = 0 . . . . . . one sign change ⇒ one positive real solution
This is a cubic equation with one positive real solution. There are several possible approaches to solving this. My favorite is to let a graphing calculator show me the solution.
You can also factor 1170 = 13*10*9, so x=10.
The width of the prism is 10 feet; the length is 13 feet; the height is 9 feet.
.. (x +3)(x)(x -1) = 1170
.. x^3 +2x^2 -3x -1170 = 0 . . . . . . one sign change ⇒ one positive real solution
This is a cubic equation with one positive real solution. There are several possible approaches to solving this. My favorite is to let a graphing calculator show me the solution.
You can also factor 1170 = 13*10*9, so x=10.
The width of the prism is 10 feet; the length is 13 feet; the height is 9 feet.