Find the initial term and common difference for the arithmetic sequence represented by the expression -9n+12.
To find the initial term and common difference for an arithmetic sequence represented by an expression, we need to write the expression in the form an + b, where "a" represents the initial term and "b" represents the common difference.
In this case, the given expression is -9n + 12. So, we need to rewrite it as an + b.
We can rewrite -9n + 12 as (-9)n + 12 to emphasize that -9 is the coefficient of n.
Now, we can say that the initial term "a" is -9 and the common difference "b" is 12.
Therefore, the initial term for the arithmetic sequence represented by -9n + 12 is -9, and the common difference is 12.
To find the initial term and common difference of the arithmetic sequence represented by the expression -9n+12, we need to rewrite the expression into the form of an arithmetic sequence.
The general form of an arithmetic sequence is given by:
an = a1 + (n-1)d
Where:
an is the nth term of the sequence
a1 is the initial term
n is the position of the term in the sequence
d is the common difference between consecutive terms.
In this case, we can equate -9n + 12 to the general form:
-9n + 12 = a1 + (n - 1)d
Comparing the coefficients of n on both sides, we get:
-9 = d
Thus, the common difference (d) of the arithmetic sequence is -9.
And to find the initial term (a1), we can substitute the common difference (-9) into the equation:
-9n + 12 = a1 + (n - 1)(-9)
Simplifying the equation, we have:
-9n + 12 = a1 - 9n + 9
Rearranging the equation, we get:
12 + 9 = a1
Thus, the initial term (a1) of the arithmetic sequence is 21.
Therefore, the initial term (a1) is 21 and the common difference (d) is -9 for the arithmetic sequence represented by the expression -9n + 12.