Lissette Arenas

Honors Pre- Calculus

April 9th, 2012 Arithmetic Sequence (Finite)

Casey decided she was going to deposit a certain amount of money in her bank account each month for 6 months. She wanted to deposit an intial amount of $5000 and then add $1000 more from the previous amount, and then deposit that amount into her account. The table below represents how much she desposited in her account each month. N 1 2 3 4 5 6

Term $5000 $6000 $7000 $8000 $9000 $10000 Recursive Formula Explicit Formula A = 5000

A = A + 1000 1 n n-1 A = A + (n-1) d

A = 5000+ (n-1) 1000

A = 5000 + 1000n- 1000

A = 4000 + 1000n n 1 n n n Summation Notation 6 k=5000 4000 + 1000n Th'm: Sum of a Finite Sequence

n (a + a ) 1 n 2 6 (5000 + 10000)

2 = 6(15000) 2 = 6 (7500) = $45000 Geometric Sequence (Finite) Jimmy decided to eat a snack while watching tv. At first, he got 1 cookie from the jar. Then, he got 2 cookies from the jar. Finally, he got the last 4 cookies from the jar. Recursive Formula Explicit Formula A = 1

A = A * 2 1 n n-1 A = a * r n 1 n-1 A = 1 * 2 n n-1 Summation Notation 3 k= 1 1 * 2 n-1 Th'm Sum of a Finite sequence

a (1-r ) 1 n 1-r = 1(1-2 )

1-2 3 = 1(1-8) = 1(-7) =7

-1 -1 Arithmetic Question Questions How to find the 10th term (how much Casey would deposit on month 10)....

Explicit formula:

A = 4000 + 1000n

A = 4000 + 1000 (10)

A = 4000 + 10000

A = $14000

On month 10, if Casey wanted to collect more money for her new car, she would have to deposit $14000. n 10 10 10 Geometric Sequence Question When would Jimmy get 64 cookies from the jar?

Explicit Formula

A = 1 * 2 N=7, so Jimmy will get 64

64 = 1 * 2 cookies the 7th time he

64 = 2 puts his hand in.

2 = 2

6 = n-1

7 = n

n n-1 n-1 n-1 6 n-1 n 1 2 3

term 1 2 4

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