-3, 12, -48, ... Write the explicit and recursive formulas for the geometric sequence. Use your explicit formula to calculate the 6th term in the sequence.
1- Identify(2pts): What is the problem? What do you need to find or do? What will your final answer look like? Do you understand what is being asked and what you need to do?
a) Finding the formulas for geometric sequence.
b) Find the common ratio and generalize the recursive form of the formula
c) Explicit: Recursive:
an = (-3)*(-4)n an = an-1(-4)
d) Opinionated question
2- Think(2pts): What have they told you? What does it mean? What more do you know or can you figure out? What connections can you make? Do you have a list of things you know, ideas to try & a plan for doing it?
a) Explicit formula uses only the number of term; Recursive formula uses the previous term
b) Explicit formula requires the data of n; Recursive formula requires the data of an-1
c) You can find the nth term directly with explicit formula, but not recursive formula
d) Recursive formula is generated by multiplying the previous term of explicit formula by one common ratio
e) Again, opinionated question
3-Do(4pts): Solve by showing steps towards completing the problem. Revise your plan if it doesn’t work the first time. Check your work.
Find the common ratio:
r = 12/(-3) = -48/12 = -4
By the formula: an = a0rn
Explicit formula: an = (-3)(-4)n
Recursive formula: an = an-1(-4)
4-Answer(2 pts): Look back at your work and answer – does it make sense, answer all of the questions, and is reasonable (accurate)? When it is - Organize and report your work and final answer
Opinionated question
From all of this "too easy question", it is to test your understanding. So, basically, just short answer will do.
