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Geometric Sequences

Geometric Sequences. Part 2. Geometric Sequences. Geometric Sequences are found by multiplying the previous term by the same number, r. The general term is found using: a n = a 1 • r n-1. Geometric Sequences. Find the 12 th term of the sequence -1, 4, -16, 64, …

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Geometric Sequences

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  1. Geometric Sequences Part 2

  2. Geometric Sequences • Geometric Sequences are found by multiplying the previous term by the same number, r. • The general term is found using: • an = a1 • rn-1

  3. Geometric Sequences • Find the 12th term of the sequence -1, 4, -16, 64, … • Find the general term first using the formula, then use the general term to find the specified term. • an = a1 • rn-1 • r = -4 and a1 = -1 • an = -1 • (-4)n-1 • a12 = -1 • (-4)11 = 4,194,304

  4. Geometric Sequences • You try a couple now: • Find the 25th term of the sequence -7, -14, -28, -56, … • -117,440,512 • Find the 7th term of the sequence 9, 3, 1, , …

  5. Geometric Sequences • Summation • Now we will use the summation formula for geometric sequences. • Sn = a1() • r = is the common ratio • n = the number of terms • a1 = the first term in the sequence

  6. Geometric Sequences • Let’s start with the easy ones: • 4 + 8 + 16 + 32 + … + 4(212) • a1 = 4 • r = 2 • n = 13 • Sn = a1() • = 4() • = 4() • = 32,764

  7. Geometric Sequences • Now to the ones that you are more familiar with: • k – 1 • a1 = 3 • n = 13 • r = 0.4 • Sn = a1() • = 3() • = 3() • ≈ 4.99997

  8. Geometric Sequences • Your turn!! • 1 + 2 + 4 + 8 + … + 1(28) 511 • 1.9998

  9. Geometric Sequences • Application time…..yahoo! • Sarah is offered a government job with the Department of Transportation. She is hired on the GS scale at a base rate of $32,000 with 1.7% increases in her salary per year. Calculate what her salary will be after she has been with the department for 12 years. • Find the general term….. • an = a1• rn-1 • a1 = 32000 • r = 1.017 • an = 32000 • 1.017n-1 • n = 12 • = 32000 • 1.01711 • = $38,519.48

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