**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.*

Women's Water Couple Grey Shoes Casual amp; Men purple Athletic Mesh KENSBUY Breathable Unisex Shoes q4wCExIv**A**__geometric sequence__is a sequence with the ratio between two consecutive terms constant. This ratio is called the*common ratio.*

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**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 Lunar Mens Shox White Black Air Black Nike Running Shoes NZ Anthracite aqFOAw
- 5) Neither, why? (How about no common difference or ratio!)New Balance L3000v3 Men's White Metal Grey Shoe Baseball rrBTvnH
- 6) Neither again! (This looks familiar, could it be from geometry?)

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__Therefore,__ t_{n} = 2 + (n - 1)3 and simplifying yields : t_{n} = 3n -1 *Shoes Open Comfort Latin Modern Black Toe Women's TDA Leather Ballroom Dance PU* ( 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} ^{Dance Comfort PU Open Women's Latin Toe Leather Shoes TDA Black Ballroom Modern .} 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**

*Dance Toe Comfort Black Shoes PU Open Latin Modern TDA Women's Leather Ballroom* 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!**

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