Find the missing terms of the arithmetic sequence 27,?,?,?,53
To find the missing terms of the arithmetic sequence, we need to determine the common difference. The common difference can be found by subtracting two consecutive terms.
The difference between 27 and the next term is unknown, so we can represent it as x. Thus, the second term can be written as 27 + x.
Similarly, the difference between the second term and the next term is also unknown, so we can represent it as x. Thus, the third term can be written as 27 + x + x = 27 + 2x.
The difference between the third term and the next term is still unknown, so we represent it as x. Thus, the fourth term can be written as 27 + 2x + x = 27 + 3x.
We know that the fourth term is 53, so we can set up the equation:
27 + 3x = 53.
Subtracting 27 from both sides of the equation, we have:
3x = 53 - 27 = 26.
Dividing both sides of the equation by 3, we get:
x = 26/3.
So the common difference is 26/3.
Now we can find the missing terms:
Second term = 27 + (26/3) = 27 + 8.67 = 35.67
Third term = 35.67 + (26/3) = 35.67 + 8.67 = 44.34
Fourth term = 44.34 + (26/3) = 44.34 + 8.67 = 52.01
Thus, the missing terms of the arithmetic sequence are 35.67, 44.34, and 52.01.