3___,___,20 (arithmetic)
To determine the missing numbers in the arithmetic sequence 3___, ___, 20, you need to find the common difference between consecutive terms.
The common difference in an arithmetic sequence is the constant value that is added or subtracted from one term to the next. We can calculate it by subtracting any term from its preceding term or by subtracting any term from its succeeding term.
Let's subtract the second term from the first term:
3 - ___ = 20 - ___
To simplify this subtraction, we need to know the value of the common difference (let's call it "d"). The equation becomes:
3 - d = 20 - (d + d)
Simplifying further:
3 - d = 20 - 2d
To isolate the "d" term, we can move the -d term to the right side of the equation and the -2d to the left side:
3 + 2d = 20
Now, subtract 3 from both sides:
2d = 20 - 3
2d = 17
Divide both sides by 2 to solve for "d":
d = 17/2
d = 8.5
Now that we have the value of the common difference (d = 8.5), we can find the missing numbers by adding or subtracting this value from the known terms.
First missing number:
3 + 8.5 = 11.5
Second missing number:
20 - 8.5 = 11.5
Therefore, the missing numbers in the arithmetic sequence 3___, ___, 20 are 11.5 and 11.5.