Presentation on theme: "8.2 Arithmetic Sequences and Series 8.3 Geometric Sequences and Series"— Presentation transcript:
18.2 Arithmetic Sequences and Series 8.3 Geometric Sequences and Series
2Arithmetic SequencesA sequence is arithmetic if the differences between consecutive terms are the same. So, the sequencea1, a2, a3, ….,anis arithmetic if there is a number d such thata2-a1= a3-a2=a4-a3=…=dThe number d is the common difference of the sequence.
7Exercises:Determine the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 22 seats in the second row, 24 in the third row and so on.Can you find the sum of an infinite arithmetic series?
8Geometric SequencesA sequence is geometric if the ratios of consecutive terms are the same. So, the sequencea1, a2, a3, ….,anis geometric if there is a number r such thata2/a1= a3/a2=a4/a3=…=rThe number r is the common ratio of the sequence.
11More examplesFind the nth term of a geometric sequence whose first term is 4 and whose common ratio is ½ .The second term of a geometric sequence is -18 and the fifth term is 2/3. Find the sixth term.