Find any term of an arithmetic sequence, given the formula of the sequence

The  exercise appears under the Algebra I Math Mission. This exercise practices finding a specific term in the sequence given an arithmetic sequence, ether in explicit form or in recursive form.

Types of Problems
There is one type of problem in this exercise:


 * 1) What is the nth term in the sequence?: This problem provides a sequence of numbers that follow an arithmetic progression. The student is asked to find the nth next number in the sequence provided.Find the next term of an arithmetic sequence, given the first few terms.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, etc.
 * 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.