? , ____ , 7, 12, 17, 22
The function of this sequence is linear. The slope of the function is 5. What number should be first in the sequence?
To find the first number in the sequence, we need to determine the pattern and the formula for the function.
The given sequence is: ? , ____ , 7, 12, 17, 22
Since the slope or the rate of change between terms is constant at 5, we can determine that the pattern is increasing by 5 with each term.
To find a formula for this linear function, we can use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n-1)d
Where:
an = the nth term
a1 = the first term
n = the term number
d = the common difference
In this case, the common difference (d) is 5.
Plugging in the values from the given sequence, we have:
7 = a1 + (3-1)5
7 = a1 + 2 * 5
7 = a1 + 10
Simplifying the equation, we get:
a1 = 7 - 10
a1 = -3
Therefore, the first number in the sequence should be -3.