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11.2 Arithmetic Sequences and Series

11.2 Arithmetic Sequences and Series. Objective : To find the sum of an arithmetic series and apply this concept to word problems and sigma notation. To find the partial sum of any arithmetic sequence, use the formula below. n = # of terms being added a 1 = 1 st term being added

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11.2 Arithmetic Sequences and Series

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  1. 11.2 Arithmetic Sequences and Series Objective: To find the sum of an arithmetic series and apply this concept to word problems and sigma notation.

  2. To find the partial sum of any arithmetic sequence, use the formula below • n = # of terms being added • a1 = 1st term being added • an = the final term being added

  3. Find the indicated nth partial sum of the arithmetic sequence. • Example 1: 3,10,17,24,31,… n = 11

  4. Find the indicated nth partial sum of the arithmetic sequence. • Example 2:

  5. Find the indicated nth partial sum of the arithmetic sequence. • Example 3:

  6. Find the partial sum • Example 4:

  7. Find the partial sum • Example 5:

  8. Practice Find each indicated sum. 1. 2.

  9. Seating Capacity Determine the seating capacity of an auditorium with 36 rows of seats if there are 15 seats in the 1st row, 18 seats in the 2nd row, 21 seats in the 3rd row, and so on.

  10. Brick Pattern A triangular brick wall is made by cutting some bricks in half to use I the first column of every other row. The wall has 28 rows. The top row is ½ brick wide. An additional ½ brick is added per row. How many total bricks will be needed to construct the wall?

  11. 11.3 – Geometric Sequences and Series Objective: To recognize and write the nth term for geometric sequences

  12. What is a geometric sequence? It is a sequence in which the ratio, r, of any two consecutive terms is constant. This ratio is called the common ratio. Determine whether each sequence is geometric. If it is, find the common ratio. Ex1. 3, 12, 48, 92, … Ex2. 5, 1, 0.2, 0.04 Ex3. 9,-6,4,-8/3,… Ex4.

  13. Given a1 and r. Given recursive sequence Write the 1st 5 terms of the geometric sequence

  14. Nth term of a geometric sequence In order to find the nth term you must know r and a1. Ex1. Ex2.

  15. Nth term of a geometric sequence Ex3. Ex4.

  16. Find the nth term Find the indicated term Practice

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