Ch.9 Sequences and Series

1. Ch.9 Sequences and Series Section 1 - Mathematical Patterns

2. Sequences Sequence: an ordered list of numbers. Each number in a sequence is a term of a sequence. We use variables with a subscript to indicate position of a number in a sequence. Ex. a5 is the 5th term in sequence a1, a2, a3, a4...

3. Cont. Subscripts usually start with 1 for the first term in the sequence. As such, an is the nth term in a sequence. 1st term 2nd term 3rd term … n-1 term nth term n+1 term... ↓ ↓ ↓ ↓ ↓ ↓ a1a2 a3an-1 an an+1

4. Representing a Pattern Explicit Formula: describs the nth term of a sequence using the number n. This formula relates the terms value to the term’s placement in the sequence.

5. EXample Ex. 2, 4, 6, 8, 10,... The nth term is twice the value of n. So an=2n is a general formula for the sequence. Any term in the sequence can be found. a1=2(1)=2, a4=2(4)=8, and a10=2(10)=20 n=1 n=2 n=3 n=4 ↓ ↓ ↓ ↓ 2 4 6 8

6. EXample 1.)Write an explicit formula for the following sequence: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28. 2.)A sequence has an explicit formula an=12n+3. What is term is a12?

7. Cont. Recursive Formula: has two parts • an initial condition: a1= starting number • recursive formula (relates each term after the first term to the one before it) a1=b an=an-1+ c, where c is the pattern

8. EXample 133, 130, 127, 124,... a1=133 an=an-1-3, for n>1

10. EXample • What is the recursive formula for the sequence? a.) 1, 2, 6, 24, 120, 720, ... b.) 1, 5, 14, 30, 55, ...