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Warm Up

Warm Up. Calculate the sum of the multiples of 7 between 11 and 391. For an arithmetic sequence, A 1 =56 and A 11 =-14. Determine S 15 . For a geometric sequence, A 1 =125, and r = -2/5. Determine S 5 . For a geometric sequence, A 1 =16, r =3/2, and S n =211. Determine n and A n .

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Warm Up

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  1. Warm Up Calculate the sum of the multiples of 7 between 11 and 391. For an arithmetic sequence, A1=56 and A11=-14. Determine S15. For a geometric sequence, A1=125, and r = -2/5. Determine S5. For a geometric sequence, A1=16, r =3/2, and Sn =211. Determine n and An.

  2. Convergent: A sequence converges if as n increases without bound, the terms of the sequence get closer and closer to some real number (called the limit). Divergent: Any sequence that does not converge.

  3. Determine whether the sequence will converge or diverge. 4, 4, 4, 4, 4, …. 2, 0, -2, 0, 2, …. 1, 2, 3, 4, 5, ….

  4. Determine whether the sequence will converge or diverge.

  5. Determine whether the sequence will converge or diverge.

  6. Discuss with your group… • Write an example of an arithmetic sequence that will diverge. • Write an example of an arithmetic sequence that will converge. • Find an example of an geometric sequence that will diverge. • Find an example of an geometric sequence that will converge.

  7. Calculating the sum of an infinite series…

  8. Infinite geometric series… Determine whether the sequence will converge. If it converges, calculate the sum.

  9. Infinite geometric series… Determine whether the sequence will converge. If it converges, calculate the sum.

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