Which two numbers should be placed in the blanks below so that the difference between consecutive numbers is the same?
19,_,_55
31 and 43
Since the difference between consecutive numbers is the same, we can calculate it by subtracting the smaller number from the larger number.
To find the difference between 19 and 55, we subtract:
55 - 19 = 36.
Now, we need to find two numbers with a difference of 36. Let's do a little math magic:
36 รท 2 = 18.
So, the two numbers that should be placed in the blanks are:
19, 37, 55.
Now that I've solved that, I can finally sit back and enjoy some number puzzles with the rest of the circus animals!
To find the two numbers that should be placed in the blanks so that the difference between consecutive numbers is the same, we need to determine the common difference.
Given the sequence 19, _, _, 55, we can start by finding the difference between the first two terms:
_ - 19 = _
Then, find the difference between the last two terms:
55 - _ = _
Since we want the difference between consecutive numbers to be the same, the result of both calculations should be equal.
Let's solve for the first blank. Assuming the common difference is represented by 'd', we have:
_ - 19 = d
Now, let's solve for the second blank, based on the assumption that the common difference remains 'd':
55 - _ = d
To find the value of 'd', we can subtract the equation we derived for the first blank (_ - 19 = d) from the equation for the second blank (55 - _ = d):
55 - _ - (_ - 19) = d
By simplifying the equation above, we get:
55 - _ - _ + 19 = d
Combining like terms, we have:
55 - 2_ + 19 = d
Simplifying further:
74 - 2_ = d
Now, let's substitute this value of 'd' back into one of the equations we formed earlier. Let's use the equation for the first blank:
_ - 19 = 74 - 2_
Simplifying the above equation:
_ - 19 = 74 - 2_
Add 19 to both sides:
_ = 93 - 2_
Finally, subtract 2 from both sides:
_ = 91
So, the two numbers that should be placed in the blanks to maintain a constant difference of the sequence 19, _, _, 55 are 91 and 91.
So you want them to be an arithmetic sequence
19 , 19+d, 19+2d, 19+3d
but 19+3d = 55
3d= 36
d = 12
etc