The California Mathematics Content Standards -Grade8 9 10 11 12 

---

Algebra II

---

Standard 22. Students find the general term and the sums of arithmetic series and both finite and infinite geometric series.

---

Skills (Note: none listed for science standards)

---

Teacher Strategy

---

Student Tasks or Scientific Investigation/Experimentation An Arithmetic Sequence (AS)is one in which the difference between any two consecutive terms is the same.A Geometric Sequence (GS)is one in which each term after the first is the product of the preceding term and the common ratio.Give four examples comparing arithmetic and geometric sequences beginning with the same term and continuing each sequence for five terms.(E.G.,AS:2,4,6,8,10 with a difference of 2;GS:2,4,8,16,32 with a common ratio of 2.)  Find the sum of the first 34 terms of the arithmetic series:24.5 +21.5 +18.5 +15.5 +…  Find the sum of the first ten terms of the geometric series 2 +4 +8 +16 +…  Find the sum of the infinite geometric series

---

Assessment or Scientific Application/Assessment

---

Resources and Technology Resource:Fibonacci Numbers in Nature is a poster that presents a fascinating exploration of number patterns in everyday objects.It comes with a four-page guide and provides historical background and detailed explanations.Fascinating Fibonaccis by Trudi H.Garland explores Fibonacci numbers, ratios and their occurrence in natural phenomena.These materials can be purchased separately or as a set through Cuisenaire ® Dale Seymour Publications ®. Technology:Algebra Online Personal Help at http://www.algebra-online.com is a website where tutors are available to help answer specific questions after you have checked the Message Board to see if your question has already been answered.Qualifications of tutors are listed (e.g.,high school mathematics teacher Geometry through Calculus;someone pursuing a degree in applied Mathematics.)

---

This page is taken from the Santa Clara Office of Education.

---