What is a progression/sequence?

• A?progression?(or?sequence) is an?ordered?set of numbers with a rule for finding all the numbers in the progression

• The numbers in a sequence are called?terms
• The terms of a progression are often referred to by letters with a subscript

What is a series?

• You get a?series?by summing up the terms in a?progression

?

• We use the notation?S_n?to refer to the sum of the first?n?terms in the progressionie.? ?S_n?=?u₁?+?u₂?+?u₃?+ …?+?u_n

Increasing, decreasing and periodic progressions

• A progression is?increasing?if?u_n+1?>?u_n?for all positive integers?n?– ie if every term is greater than the term before it
• A progression is?decreasing?if?u_n+1?<?u_n?for all positive integers?n?– ie if every term is less than the term before it

• A progression is?periodic?if the terms repeat in a cycle
• The?order?(or?period) of a periodic progression is the number of terms in each repeating cycle