Arithmetic series

The  exercise appears under the Precalculus Math Mission. This exercise experiments with recursive and explicit forms of arithmetic sequences to find the answers to series.

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


 * 1) Find the sum of the recursively defined sequence: This problem provides a recursive rule for an arithmetic sequence. The student is expected to use the rule and find the sum of a specified number of terms of the sequence.Ariser2.png
 * 2) Find the sum of the explicitly defined sequence: This problem provides an explicit rule for a arithmetic sequence. The student is expected to use the rule to find the sum of a specified number of terms of the sequence.Ariser1.png

Strategies
Knowledge of formulas and patterns from arithmetic sequences and series are encouraged to ensure success on this exercise.
 * 1) The sum of the terms in a sequence is called a series.
 * 2) For a recursive formula, the general strategy involves finding the first term, plugging that in to get the second, plugging that in to get the third, et cetera.
 * 3) Generally, the nth term of a arithmetic sequence is given by $$ a_n=a_1+(n-1)d$$ where a_1 is the first term and d is the difference between successive terms.
 * 4) The sum of an arithmetic sequence is given by $$ S_n=\frac{n(a_1+a_n)}{2}=\frac{n(2a_1+(n-1)d}{2}$$.

Real-life Applications

 * 1) Sequences are series are fundamental to the calculus, which has many applications to real life.
 * 2) Sequences are common on IQ tests for measuring pattern recognition ability.
 * 3) Taylor Series can be used to approximate complicated functions via polynomials.
 * 4) Arithmetic sequences appear in the study of linear relationships, the common difference acts like a slope.