1,8,81,16,__,1296
if you answer correctly will mark you as brainliest
Answers
Answer: The answer is 256.
Step-by-step explanation:
1. Find connections
Try to find connections between the numbers or between each number and its place in the sequence.
One pattern found:
14=1
24=16
34=81
?
54=625
64=1296
2. Analyze
You can see that three numbers are involved in each equation.
The first changes, and changes by 1 each time. Call it x .
The second number remains constant, and therefore will be the same in each: 4 .
The third is a product of the other side of the equation.
Therefore, we can construct the following formula for discovering the pattern:
f(x) =x4
where x is the place in the sequence, and f(x) or y is the output of x .
3. Solve
We want to find the fourth number in the sequence. In other words, the place of the number in the sequence we want to find is 4 .
So we substitute x with 4 in the formula:
f(x) =44
Compute.
f(x) = 256
The answer is 256.
(Alternatively, you could have graphed it and saw that the line intercepts the x-axis 4 times. Therefore, with the Fundamental Theorem of Algebra, you would have known that the formula is f(x) =x4 .)