The next three terms are: 1/6 , 0 and -1/6
Step-by-step explanation:
Given sequence is:

First of all, we have to find the common difference

The common difference is -1/6
We can simply add -1/6 to the previous term to find the next terms so,
Adding -1/6 to 1/3

Hence,
The next three terms are: 1/6 , 0 and -1/6
Keywords: Arithmetic sequence, common difference
Learn more about arithmetic sequence at:
#LearnwithBrainly
 
        
             
        
        
        
Check the forward differences of the sequence.
If  , then let
, then let  be the sequence of first-order differences of
 be the sequence of first-order differences of  . That is, for n ≥ 1,
. That is, for n ≥ 1,

so that  .
.
Let  be the sequence of differences of
 be the sequence of differences of  ,
,

and we see that this is a constant sequence,  . In other words,
. In other words,  is an arithmetic sequence with common difference between terms of 2. That is,
 is an arithmetic sequence with common difference between terms of 2. That is,

and we can solve for  in terms of
 in terms of  :
:



and so on down to

We solve for  in the same way.
 in the same way.

Then



and so on down to


 
        
             
        
        
        
Answer:
on example 1, both are right triangles.
 
        
             
        
        
        
40% of 50 is 20. 
20 is 25% of 80.
So the answer you are looking for is 25%.
 
        
             
        
        
        
Answer:
x = 5, -3
Step-by-step explanation:
2x² - 4x - 5 = 25
add 5 to each side
2x² - 4x = 30
factor out the 2
2(x² - 2x) = 30
divide both sides by 2
x² - 2x = 15
divide b by 2, square it -- (b/2)², and add it to both sides
-2/2 = -1 → -1² = 1
x² - 2x + 1 = 15 + 1
factor the expression on the left -- this will be [x - (b/2)]²
(x - 1)² = 16
find the square root of both sides
x - 1 = ±4
add 1 to both sides
x = 4 + 1
x = -4 + 1
solve
x = 5, -3