Question

Can someone please help me do this, I really don't understand it...

a1 = -4, an = an-1 + 7

Answer 1

This is a sequence.
It is not hard, but you need to understand the notation.
A sequence is a set of numbers.
The first number of the sequence is called \(a_1\). The second number is called \(a_2\). Then the next numbers are \(a_3, a_4, \) etc.
\(a_1\) is read "a sub 1."

Answer 2

What are you trying to find, the series of numbers? an-1...what number does n have to be to get a1? That way you can find your an while using a1. Then you'll get the next an to put into the equation to find the next number and the next.

Answer 3

The question is which numbers are in the sequence?
The problem is telling you a rule that will tell you how to figure out which numbers to have in the sequence and in what order.

Answer 4

The problem states: \(a_1 = -4\).
This tells you the first number of the sequence is -4.

Answer 5

The next part of the problem tells you what the rule is to find the next number in the sequence.
In this case, the rule is: \(a_n = a_{n-1} + 7\).
Read this as "a sub n equals a sub n minus 1 plus 7."

Answer 6

The rule is telling you that for any number in the sequence after the first one, let's say it's the nth term, the rule to follow is that the nth term is the (n - 1)th term plus 7. All that means is that any new term is the previous term plus 7.

That means
\(a_1 = -4\)
\(a_2 = a_1 + 7 = -4 + 7 = 3\)
\(a_3 = a_2 + 7 = 3 + 7 = 10\)
\(a_4 = a_3 + 7 = 10 + 7 = 17\)
etc.

Answer 7

Oh!! OhKay! I get it now!

Answer 8

@mathstudent55 , Just to make sure I get the hang of it, it would be something like:

a1 = 6, an = 2 • an-1
2*6=12
2*12=24
2*12=48
2*48=96
2*96=192

Answer 9

Correct. In this case you start with 6.
Each subsequent term is 2 times the previous term.

Answer 10

Oh my god! I love you so much right now, thanks!!

Answer 11

The concept is simple, but you need to get used to the notation.
When you see \(a_n = 2 \cdot a_{n - 1} \) for the first time, it's hard to understand what it means. Once you understand the notation, all it means is take the first term, multiply it by 2 to get the second term. Then keep multiplying each new term you find by 2 to find the next one.

Answer 12

You're welcome.