Answer:
The general rule of the progression is an = 3n - 10
Step-by-step explanation:
Given
Type of progression: Arithmetic Progression
a7 = 11
d = 3
Required.
The rule
First, we write out the formula of an arithmetic progression.
This is as follows
an = a + (n - 1)d
The given data is when n = 7.
So, by substituting the values in the formula above, we have
a7 = a + (n - 1)d
11 = a + (7 - 1) * 3
11 = a + 6 * 3
11 = a + 18
Make a the subject of formula
a = 11 - 18
a = -7
Having gotten the value of a, the general rule is gotten by substituting the value of a and d in the formula.
In other words,
an = a + (n - 1)d becomes
an = -7 + (n - 1)3
Open bracket
an = -7 + 3n - 3
Collect like terms
an = -7 -3 + 3n
an = -10 + 3n
Rearrange
an = 3n - 10
Hence, the general rule of the progression is an = 3n - 10
