The sum of the first 8 terms is 2.51 to the nearest hundredth
Step-by-step explanation:
In the geometric sequence there is a constant ratio between each two consecutive terms
The formula of the sum of n terms of a geometric sequence is:
, where
- a is the first term
- r is the constant ratio between the consecutive terms
∵ The sequence is 6 , -5 , 25/6 , .............
∵ -5 ÷ 6 = 
∵ 
÷ -5 =
- There is a constant ratio between the consecutive terms
∴ The sequence is a geometric sequence
∵ The first term is 6
∴ a = 6
∵ The constant ratio is
∴ r =
∵ We need to find the sum of 8 terms
∴ n = 8
- Substitute the values of a, r and n in the rule above
∴ ![S_{8}=\frac{6[1-(\frac{-5}{6})^{8}]}{1-(\frac{-5}{6})}](https://tex.z-dn.net/?f=S_%7B8%7D%3D%5Cfrac%7B6%5B1-%28%5Cfrac%7B-5%7D%7B6%7D%29%5E%7B8%7D%5D%7D%7B1-%28%5Cfrac%7B-5%7D%7B6%7D%29%7D)
∴ 
- Round it to the nearest hundredth
∴ 
The sum of the first 8 terms is 2.51 to the nearest hundredth
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
#LearnwithBrainly
I’m pretty sure that the figure is a rectangle and the two longer sides are 9 centimeters and the shorter ones are 6 centimeters. Rectangles have 4 right angles and all of the side lengths added together equals 30 centimeters
This is the answer I wish you will understand
When it says 7 more than a number equals 21, the "more than" is addition, a number is x (because it's the unknown number). So this one is x+7=21.
When it says 39 less than a number is 21. "Less than" means to subtract. The 39 is less than x, so it's x-39=21.
8 times a certain number increased by 1 is 65. Break it down, first 8 times a number, so it's 8*x or 8x. Then we add 1 to that, so it's 8x+1=65.
5 times some number decreased by 2 times the number is 42. Decreased by is subtraction. So it's 5x-2x=42.
When you look for the key words increased by (add), more than (add), multiplied by, times, less than (subtract), decreased by (subtract), is (equal sign), they will help determine what you need to do.
I hope this gives you a little more understanding. Good luck with it! :)
I'm super rusty and not very good in slope intercept and I don't want to mess you up, but this video from Khan Academy (https://m.youtube.com/watch?t=215s&v=IL3UCuXrUzE) helped me understand it, you should check it out.
