2. Is there a common DISTANCE or common RATIO? Watch out for the word AFTER. “After 1 year” can mean T2, after 2 years can be T3 Write the sequence Tn or Sn? Term or Sum? Make sure you write the right formula!!

3. I buy a car for $9990. Every year it depreciates 10%. What will it be worth after 6 years? 10% decrease….next term is worth 90% R = 0.9 I buy a car for $9990. Every year it depreciates 10%. What will it be worth after 6 years? T6 is AFTER 6 years So T1 is AFTER 1 year Either calculate T7 or make Term 1… T1 = $9990 x 0.9 = $8991

4. I buy a car for $9990. Every year it depreciates 10%. What will it be worth after 6 years? We are not asked for a total, so use Tn Tn = ar n-1 T6 = 8991 x 0.9 6-1 T6 = 8991 x 0.9 5 T6 = 5309.09559 ANSWER: $5309.10

5. Cleo’s grandmother gives her a Barbie doll when she turns 8. She gives her 3 Barbies when she turns 9. Every year, Cleo’s grandmother increases the size of her birthday gift by 2 more Barbies! How many Barbies will Cleo have when she is 13? The sequence is 1, 3, 5,… there is a common DIFFERENCE of 2. The sequence is ARITHMETIC

6. Cleo’s grandmother gives her a Barbie doll when she turns 8. She gives her 3 Barbies when she turns 9. Every year, Cleo’s grandmother increases the size of her birthday gift by 2 more Barbies! How many Barbies will Cleo have when she is 13? If Cleo is 8 for T1, she will be 9 for T2…. Cleo turning 13 means we want T6

7. Cleo’s grandmother gives her a Barbie doll when she turns 8. She gives her 3 Barbies when she turns 9. Every year, Cleo’s grandmother increases the size of her birthday gift by 2 more Barbies! How many Barbies will Cleo have when she is 13? The question is not how many she’s GIVEN that year. It is how many she will HAVE. It is a total, so use Sn.

8. Cleo’s grandmother gives her a Barbie doll when she turns 8. She gives her 3 Barbies when she turns 9. Every year, Cleo’s grandmother increases the size of her birthday gift by 2 more Barbies! How many Barbies will Cleo have when she is 13? Sn = n/2 [ 2a + (n-1)d] S6 = 3 [ 2 + 5x2] S6 = 3 x 12 S6 = 36 ANSWER: 36 Barbies

9. James gets a job as a door-to-door salesman. In the first week, he sells 3 vacuum-cleaners. In the second week he sells 5 vacuum-cleaners, in the third week he sells 7, and so on. How many will he sell a)In the 8 th week b)In the first 10 weeks? James gets a job as a door-to-door salesman. In the first week, he sells 3 vacuum-cleaners. In the second week he sells 5 vacuum-cleaners, in the third week he sells 7, and so on. How many will he sell a)In the 8 th week? b)In the first 10 weeks? T8 is in the 8 th week T1 is in the 1 st week So 3 IS T1

10. James gets a job as a door-to-door salesman. In the first week, he sells 3 vacuum-cleaners. In the second week he sells 5 vacuum-cleaners, in the third week he sells 7, and so on. How many will he sell a)In the 8 th week? b)In the first 10 weeks? T8, use Tn formula (altogether). S10, use Sn formula. If it was T10, question would say “in the 10 th week” – 1 week only.

11. James gets a job as a door-to-door salesman. In the first week, he sells 3 vacuum-cleaners. In the second week he sells 5 vacuum-cleaners, in the third week he sells 7, and so on. How many will he sell a)In the 8 th week? b)In the first 10 weeks? A = 3 d = 2 a) Tn = a + (n-1)d T8 = 3 + (8-1)2 T8 = 3 + 7x2 T8 = 17 ANSWER = 17 vacuum cleaners

12. James gets a job as a door-to-door salesman. In the first week, he sells 3 vacuum-cleaners. In the second week he sells 5 vacuum-cleaners, in the third week he sells 7, and so on. How many will he sell a)In the 8 th week? b)In the first 10 weeks? A = 3 d = 2 b) Sn =n/2[ 2a + (n-1)d] S10 = 5[ 6 + (10-1)2] S10 = 5[ 6 + 18] S10 = 120 ANSWER = 120 vacuum cleaners