Pre Calc Arithmetic and Geometric Sequences
Evaluate each infinite geometric series
*REMEMBER if the absolute value of the number in parentheses is above one say "no sum" Otherwise use Sn= a^1/(1-r) If there is a number outside of the parenthesis it is a^1 unlike r it does not have an exponent
For each sequence state if it is arithmetic, geometric, or neither.
Arithmetic: has a difference, meaning each number adds the same amount to get to the next. Geometric: Has a ratio, meaning each number multiplies the same amount to get to the next number Neither: No pattern between the numbers
Evaluate each series (when given as a summation)
Calculator
Given the two terms in the arithmetic sequence find the common difference and the explicit.
For this, use the arithmetic explicit formula: a^n= a^1 + (n-1)d *Don't forget to find a^1, find the difference, and distribute once you put it all back into the formula
Determine the number of terms n in each arithmetic sequence
Plug in values to Sn= n(first term + a^n/2) solve for n
Rewrite each series as a sum
Plug in whatever number is on the bottom of the summation for the variable, plug in these numbers in sequence until you reach the number on top of the summation. Write each number you found in order with a plus sign separating them.
Determine the common ratio of the infinite geometric series
Plug it in to the equation Sn= a^1/(1-r) *solve for r
Evaluate each geometric series described
Sn= first term(1-r^n)/(1-r) *if n value is not given then solve using explicit formula
Determine the number of terms n in each geometric series.
Sn= first term(1-r^n)/(1-r) Solve for n with crazy exponent thing, or logs
Evaluate each arithmetic series described
Sn= n(first term + a^n/2) If a^n is not given, plug in values to the explicit formula to find it.
Rewrite each series using sigma notion
The number on top count how many numbers are separated by plus signs. The number on bottom is always x=1. On the right side of the sigma notion write the equation needed to find each term. *remember the equation is often (first term in series)^x
Find the common ratio and the explicit formula.
a^n = a^1 (d)^n-1
Find the missing term or arm in each arithmetic sequence.
last term minus first term divided by the number of blanks plus one
