Write the rule for the arithmetic sequence if a7=11 and d=3

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