Arithmetic & Geometric Sequences!

*Sequence-a list of numbers. Two types of sequences: --Arithmetic sequence-made by adding the same positive or negative interger to generate the sequence -Fromula tn=t1=(n-1) d -t1=first term -n=term # -d=difference (what is being added or subtracted) -tn=last term --Geometric sequence-made by mulitiplying by the same whole number or fraction to generate a sequence. -Fromula tn=t1 * r ^(n-1) -r=ratio the number that is mulitiplied to generate the sequence -t1=first term -n=term # (tn= ___ term) There are many ways to generate a sequence using these formulas or to find the formula for a sequence of numbers. _____________________________________________________ Ex.1: Find a formula for tn. 1, 4, 7, 10, ... d=3 t1=1 n=n tn=t1+(n-1)d 1+(n-1)3 =1+3n-3 tn=3n-4 Ex.2: Is the following sequence arithmitic or geometric? Find the formula for the nth term. 3,5,7,9,11... This would be arithmitic because we are adding 2. Therefore d = 2. To find the formula for the nth term we need to plug numbers into the formula: tn = t1 + (n-1)d tn = 3 + (n-1)2 tn = 3 + 2n - 2 tn=2n+1