Recursive Series and Summations

Finding the general term of a sequence can be difficult. You are looking for a pattern and then giving it a mathematical equation. Two things that will help are: If a sequence is negative, positive, negative, positive, use (-1) n If a sequence is positive, negative, positive, negative, use (-1) n+1. Break down each sequence and see if you can find the pattern. Sometimes, it just takes luck…….Sorry 

The sequence alternates between negative and positive so use (-1) n. If you look for a pattern, you see 1 = 1 2 ; 4 = 2 2 ; 9 = 3 2, so the pattern is? What stays the same each time? What is the pattern with the denominator?

A recursive sequence is a sequence that uses the previous number in the sequence to find the next number in the sequence. The most famous recursive sequence is a Fibonacci sequence. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … 1+1 = 2; = 3; = 5; = 8, ….. It is the pattern that many things in nature follow: Flower petals, sunflowers, broccoli

*Due to an issue with this program, the problem looks slightly different than what you will see. The problems you will see have the i= 0 and the 4 above and below the sigma.