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Bellwork

Bellwork. A) Write the explicit expression (equation) for the following arithmetic sequence, then find the 10 th term: 6, 3, 0, -3, … B) Write the explicit expression (equation) for the following geometric sequence, then find the 10 th term: 1, 5, 25, 125, ….

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Bellwork

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  1. Bellwork A) Write the explicit expression (equation) for the following arithmetic sequence, then find the 10th term: 6, 3, 0, -3, … B) Write the explicit expression (equation) for the following geometric sequence, then find the 10th term: 1, 5, 25, 125, …

  2. A) Write the explicit expression (equation) for the following arithmetic sequence, then find the 10th term: 6, 3, 0, -3, …

  3. B) Write the explicit expression (equation) for the following geometric sequence, then find the 10th term: 1, 5, 25, 125, …

  4. End in Mind: Work with a partner to complete • You are filling a 200 gallon tank of water with a large hose. After some time passes the gauge shows that there is now 35 gallons in the tank. You're not sure how long ago you started filling it, so you leave and come back exactly 15 minutes later and see that it is now filled to 105 gallons. How long do you have until the tank begins to overflow?

  5. Arithmetic: Determine the explicit expression given the common difference and a term What do we already know? What do we need to know? The 5th term is 19. What is the first term? The common difference is +6. Plug in what you know to figure out what you don’t!

  6. Arithmetic: Determine the explicit expression given the common difference and a term a5=19 d=6 19=a1+(5-1)6

  7. Arithmetic: Determine the explicit expression given the common difference and a term Now Simplify, and solve for a1 19=a1+(5-1)6 Plug in what you know to write the explicit expression 19=a1+(4)6 an=-5+(n-1)6 19=a1+24 -24 -24 -5=a1 Remember- This was given to begin with!

  8. Arithmetic: Determine the explicit expression given the common difference and a term Now we just need to simplify! an=-5+(n-1)6 an=-5+6n-6 an=6n-11

  9. Arithmetic: Determine the explicit expression given the 1st term and another term What do we already know? What do we need to know? The 1st term is -8. What is the common difference? The 6th term is 22. Plug in what you know to figure out what you don’t!

  10. Arithmetic: Determine the explicit expression given the 1st term and another term a1=-8 a6=22 22=-8+(6-1)d

  11. Arithmetic: Determine the explicit expression given the 1st term and another term Now Simplify, and solve for d 22=-8+(6-1)d Plug in what you know to write the explicit expression 22=-8+5d +8 +8 an=-8+(n-1)6 30=5d 5 5 Remember- This was given to begin with! 6=d

  12. Arithmetic: Determine the explicit expression given the 1st term and another term Now we just need to simplify! an=-8+(n-1)6 an=-8+6n-6 an=6n-14

  13. Arithmetic: Determine which term a value is given the explicit expression for the sequence What do we already know? What do we need to know? The nth term is 65 What is n? What member of the sequence is 65? The explicit expression is an=3n+2 Plug in what you know to figure out what you don’t!

  14. Arithmetic: Determine which term a value is given the explicit expression for the sequence 65=3n+2 -2 -2 63=3n 33 21=n 65 is the 21stterm in the sequence

  15. Geometric: Determine the explicit expression given the common difference and a term What do we already know? What do we need to know? The 4th term is 1296. What is the first term? The common ration is +6. Plug in what you know to figure out what you don’t!

  16. Geometric: Determine the explicit expression given the common difference and a term a4=1296 r=6 an=a1rn-1 1296=a164-1

  17. Geometric: Determine the explicit expression given the common difference and a term Now Simplify, and solve for a1 1296=a164-1 Plug in what you know to write the explicit expression 1296=a163 an=66n-1 1296=a1216 216 216 Remember- This was given to begin with! We just found this! 6=a1

  18. Geometric: Determine the explicit expression given the 1st term and another term What do we already know? What do we need to know? The 1st term is 2. What is the common ratio? The 5th term is 1250. Plug in what you know to figure out what you don’t!

  19. Geometric: Determine the explicit expression given the 1st term and another term a1=2 a5=1250 an=a1rn-1 1250=2r5-1

  20. Geometric: Determine the explicit expression given the 1st term and another term Now Simplify, and solve for r 2, 10, 50, 250, 1250 or 2, -10, 50, -250, 1250 1250=2r5-1 1250=2r4 2 2 an=a1rn-1 625=r4 an=25n-1 an=2(-5)n-1 or

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