The simple formula for the nth term of an arithmetic sequence is an = 4n + 16. What is the explicit formula corresponding to the simple formula?
1 th term
a1 = 4 * 1 + 16 = 4 + 16 = 20
2 th term
a2 = 4 * 2 + 16 = 8 + 16 = 24
3 th term
a3 = 4 * 3 + 16 = 12 + 16 = 28
4 th term
a4 = 4 * 4 + 16 = 16 + 16 = 32
etc.
Arithmetic sequence with first term
a1 = 20
and common difference d = 4
General formula for arithmetic sequence :
an = a1 + ( n - 1 ) * d
In this case :
an = 20 + ( n - 1 ) * 4
Write the explicit formula for the geometric sequence.
a1 = -5 a2 = 20 a3 = -80
To find the explicit formula corresponding to the simple formula an = 4n + 16, we need to rewrite it in a form that expresses the nth term of the arithmetic sequence explicitly in terms of n.
The simple formula an = 4n + 16 represents the arithmetic sequence where each term is found by adding 4n to 16. In the explicit formula, we want to find a way to directly express the nth term without relying on previous terms.
To do this, we need to isolate the variable n on one side of the equation. Let's rearrange the equation:
an = 4n + 16
Subtract 16 from both sides:
an - 16 = 4n
Now, subtract 4n from both sides:
an - 4n = 16
Combine like terms:
-3n = 16
To get the explicit formula, we need to solve for n. Divide both sides of the equation by -3:
n = -16/3
So, the explicit formula for the arithmetic sequence can be written as:
an = 4(-16/3) + 16
Simplifying further:
an = -64/3 + 16
Combining fractions:
an = (-64 + 48)/3
Simplifying:
an = -16/3
Therefore, the explicit formula corresponding to the simple formula an = 4n + 16 is:
an = -16/3