Explicit formulas for arithmetic sequences

The  exercise appears under the Algebra I Math Mission and Precalculus Math Mission. This exercise increases familiarity with the explicit formula for arithmetic sequences.

Types of Problems
There are two types of problems in this exercise:


 * 1) Determine who wrote the right formula: This problem provides two proposed explicit formulas for an arithmetic sequence. The student is asked to determine which, if either, of the formulas are correct based on the given information.Effas1.png
 * 2) Determine the explicit formula: This problem provides an arithmetic sequence given in some form like a table or by listing terms. The student is asked to write a correct explicit formula in the space provided.Effas2.png

Strategies
Knowledge of the arithmetic sequence and series formulas are encouraged to ensure success on this exercise.
 * 1) The nth term of an arithmetic sequence is given by a_n=a_1+(n-1)d.
 * 2) The formula does not need to be distributed or simplified on this exercise to be considered correct.
 * 3) The formulas provided in Determine who wrote the right formula can often be determined by plugging in 1 and seeing which formula yields the correct result.
 * 4) It can be more efficient to provide the difference first when writing the explicit formula.

Real-life Applications

 * 1) Sequences and series are common problem on IQ tests.
 * 2) Sequences and series are a large portion of second semester (BC) calculus.
 * 3) The first problem type in this exercise can be considered a real-life application in the context of teachers and presenters.