13-1 Arithmetic and Geometric Sequences

Okayyy, so this week I am going to teach you how to work arithmetic and geometric sequence problems. It might seem complicating at first, but it is actually very easy and quick to learn. First, i have to give you some basic notes and formulas that you are going to need.

Notes:

• Arithmetic Sequence is a sequence that is generated by adding the same number ech time.
• The formula for arithmetic is tn=t1 + (n-1) x d
• d= what is being added or the difference.
• tn= blank terms

• Geometric Sequence is a sequence that is generated by mulitplying the same number each time.
• The formula for geometric is tn=t1 x r^(n-1)
• r= what is being mulitplied
• n=term number
• tn=blank terms

A sequence is a list of numbers.

Okay, so now that you know all what you need to, I am going to work a few examples for you.

Example 1: tn=2n + 3. Figure out the sequence and if it is geometric, arithmetic, or neither.

• You would plug in the number of terms for n.
• 2(1) + 3 = 5
• 2(2) + 3 = 7
• 2(3) + 3 = 9
• 2(4) + 3 = 11
• From that you can tell that the sequence is arithmetic because it is adding 2 to get to the next number.

Example 2: tn=3 x 2^n. Figure out the sequence and if it is geometric, arithmetic, or neither.

• You would do the same thing as in example one.
• 3 x 2^(1)= 6
• 3 x 2^(2)= 12
• 3 x 2^(3)= 24
• 3 x 2^(4)= 48
• From that you can tell that the sequence is geometric because it is mulitiplying 2 to get the next number.

So that is how you work those types of problem. Byeee.

--Halie !