Writing and Using Explicit Rules for Arithmetic Sequences

Let's visualize the information we have been given.

a_{1} \to + 2 a_{2} \to + 2 a_{3} \to + 2 8

To get to the fourth term, we have to add

2

three times to

a_{1}

.

a_{1} + 2 + 2 + 2 = 8 \Leftrightarrow a_{1} + 2 \cdot 3 = 8

Now we have an equation for

a_{1}

that we can solve.

a_{1} + 2 \cdot 3 = 8

a_{1} + 6 = 8

LHS - 6 = RHS - 6

a_{1} = 2

The first term is

2 .

Writing and Using Explicit Rules for Arithmetic Sequences 1.6 - Solution