Sequences and Series Flashcards
1
Q
How do you approach geometric sequence questions that don’t tell you u1 or r?
A
- Create the un equation for each term. (So you will have two equations.)
- Then divide the formulas from each other to eliminate u1 and solve for r.
- Plug r back into an equation to find u1.
- Now you have all the information to use the formulas to find what you’re looking for.
2
Q
How do you approach arithmetic sequence questions that don’t tell you u1 or d?
A
- Create the un equation for each term. (So you will have two equations.)
- Then subtract the formulas from each other to eliminate u1 and get the d.
- Plug d back into an equation to find u1.
- Now you have all the information to use the formulas to find what you’re looking for.
3
Q
How to find u1 and r when given three consecutive terms of a geometric sequence (and there are variables in these terms).
A
- Create and equation where
- Left side is last term divided by middle
- Right side is middle term divided by first
- Solve the equation
4
Q
How do you find “all positive terms” of an arithmetic sequence that are less than some value (for example, 100)?
A
- Find u1 and d.
- Find the nth term that is less than the value (in this case solve un=100). This tells us how many terms to add together.
- Plug this information into the sum formula to add together all of the terms (and take away any negative terms if necessary).
5
Q
What do you do when you have a problem that combines arithmetic and geometric sequences?
A
- Create expressions for the terms of the arithmetic sequence (u1, u1+d, u1+2d, etc)
- Use these expressions when creating equations for the terms of the geometric sequence.
Note that the way to approach the geometric is the same as normal.- If there are 2 terms that are not u1, create 2 equations and divide.
- If there are 3 consecutive terms, create that equation with two fractions.
- Solving step 2 should find you either u1 or d.
