Question

Help please fill out empty spots

Answer 1

Answer:

See the attached image below for the filled out chart.

• First box = 0.1
• Second box = 0.1
• Third box = 4
• Fourth box = -3
• Fifth box = 3
• Sixth box = -1

===================================================

Explanation:

Part 1

Pick any term and subtract off its previous term

So for instance 4.2 - 4.1 = 0.1

Or you could say 4.3-4.2 = 0.1

Whichever pair you pick, you should find that the common difference is 0.1

This means we add 0.1 to each term to get the next term. Therefore, the recursive rule is $a_n = a_{n-1} + 0.1$ which says "add 0.1 to the (n-1)th term to get the nth term". The (n-1)th term is the term just before the nth term.

The first term is $a_1 = 4$ as shown in the given sequence 4, 4.1, 4.2, ...

------------------------------

Part 2

We'll follow the same idea as part 1.

Subtract any two adjacent terms

-10-(-7) = -10+7 = -3

We add -3 to each term to get the next. This is the same as subtracting 3 from each term, which is reflected in $a_n = a_{n-1}-3$

The first term is $a_1 = -1$

Everything is summarized in the diagram below.