Answer:
a(9) = 150*(0.4)^8 = 0.098304
Step-by-step explanation:
This is a geometric sequence, because each new term is 0.4 times the previous term.
The general formula for a geometric sequence is a(n) = a(1)*r^(n - 1). Here, with a(1) = 150 and r = 0.4, we have:
a(n) = 150*(0.4)^(n - 1), and so
a(9) = 150*(0.4)^8 = 0.098304
Answer: 
<u>Step-by-step explanation:</u>
![\ \ \dfrac{3}{4}-x\bigg(\dfrac{1}{2}-\dfrac{5}{8}\bigg)+\bigg(-\dfrac{3}{8}x\bigg)\\\\\\=\dfrac{3}{4}\bigg(\dfrac{2}{2}\bigg)-x\bigg[\dfrac{1}{2}\bigg(\dfrac{4}{4}\bigg)-\dfrac{5}{8}\bigg]+\bigg(-\dfrac{3}{8}x\bigg)\\\\\\=\dfrac{6}{8}-x\bigg(\dfrac{4}{8}-\dfrac{5}{8}\bigg)-\dfrac{3}{8}x\\\\\\=\dfrac{6}{8}-x\bigg(-\dfrac{1}{8}\bigg)-\dfrac{3}{8}x\\\\\\=\dfrac{6}{8}+\dfrac{1}{8}x-\dfrac{3}{8}x\\\\\\=\dfrac{6}{8}-\dfrac{2}{8}x\\\\\\=\dfrac{3}{4}-\dfrac{1}{4}x\quad \text{(reduced both fractions)}](https://tex.z-dn.net/?f=%5C%20%5C%20%5Cdfrac%7B3%7D%7B4%7D-x%5Cbigg%28%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B5%7D%7B8%7D%5Cbigg%29%2B%5Cbigg%28-%5Cdfrac%7B3%7D%7B8%7Dx%5Cbigg%29%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B3%7D%7B4%7D%5Cbigg%28%5Cdfrac%7B2%7D%7B2%7D%5Cbigg%29-x%5Cbigg%5B%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%28%5Cdfrac%7B4%7D%7B4%7D%5Cbigg%29-%5Cdfrac%7B5%7D%7B8%7D%5Cbigg%5D%2B%5Cbigg%28-%5Cdfrac%7B3%7D%7B8%7Dx%5Cbigg%29%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B6%7D%7B8%7D-x%5Cbigg%28%5Cdfrac%7B4%7D%7B8%7D-%5Cdfrac%7B5%7D%7B8%7D%5Cbigg%29-%5Cdfrac%7B3%7D%7B8%7Dx%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B6%7D%7B8%7D-x%5Cbigg%28-%5Cdfrac%7B1%7D%7B8%7D%5Cbigg%29-%5Cdfrac%7B3%7D%7B8%7Dx%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B6%7D%7B8%7D%2B%5Cdfrac%7B1%7D%7B8%7Dx-%5Cdfrac%7B3%7D%7B8%7Dx%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B6%7D%7B8%7D-%5Cdfrac%7B2%7D%7B8%7Dx%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B3%7D%7B4%7D-%5Cdfrac%7B1%7D%7B4%7Dx%5Cquad%20%5Ctext%7B%28reduced%20both%20fractions%29%7D)
It should be 0.4 or 4/10 or 2/5