**A**__sequence__is a set of numbers, called terms, arranged in some particular order.**An**__arithmetic sequence__is a sequence with the difference between two consecutive terms constant. The difference is called the*common difference.*

**A**__geometric sequence__is a sequence with the ratio between two consecutive terms constant. This ratio is called the*common ratio.*

**Arithmetic formula: t**_{n}= t_{1 }+ (n - 1)d

**Geometric formula: t**_{n}= t_{1}^{.}r^{(n - 1)}

Here's the answers to the 6 questions up stairs.

- 1) Arithmetic, the common difference d = 5
- 2) Geometric, the common ratio r = 2
- 3) Geometric, r = 1/2
- 4) Arithmetic, d = -4
- 5) Neither, why? (How about no common difference or ratio!)
- 6) Neither again! (This looks familiar, could it be from geometry?)

__Therefore,__
t_{n}
= 2 + (n - 1)3 and simplifying yields : t_{n}
= 3n -1 ( tada!)

__Therefore,__
t_{n} = 4 ^{.} 2^{(n - 1)} and simplifying
gives
us: t_{n} = 2^{.}2^{n}
(Yikes stripes!
Where did this
come from. rewrite 2^{(n - 1)} as 2^{n} ^{.}
2^{-1} and cancel with the four!)

**Then as this sequence:[(2)(10)
+1],[(2)(100) +1], [(2)(1000)
+1], [(2)(10000) +1]**

**Wait! Hold on here! I see a
pattern!
Cool, without a formula! Powers of 10!**

**How does this grab
ya!
t _{n} = 2^{.}10^{n}
+ 1 Does this work? Try it and see!**

**
24 = 6d means d = 4**

**t _{53} = 5 + 52^{.}4 =
213**

** Use the
formula: 900
= 36 + 9(n - 1) and solve for n!**

**
864 = 9n - 9**

**
873 = 9n**

**
97 = n There are 97 multiples in the range!**