11X1 T14 02 geometric series (2010)
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11X1 T14 02 geometric series (2010)

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11X1 T14 02 geometric series (2010) 11X1 T14 02 geometric series (2010) Presentation Transcript

  • Geometric Series
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term.
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r.
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T r 2 a
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T r 2 a T  3 T2
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T r 2 a T  3 T2 Tn r Tn1
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T  3 T2 Tn r Tn1
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar T  3 T2 Tn r Tn1
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar  T3 T3  ar 2 T2 Tn r Tn1
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar  T3 T3  ar 2 T2 Tn  ar n1 Tn r Tn1
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar  T3 T3  ar 2 T2 Tn  ar n1 Tn r Tn1 e.g.i  Find r and the general term of 2, 8, 32, 
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar  T3 T3  ar 2 T2 Tn  ar n1 Tn r Tn1 e.g.i  Find r and the general term of 2, 8, 32,  a  2, r  4
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar  T3 T3  ar 2 T2 Tn  ar n1 Tn r Tn1 e.g.i  Find r and the general term of 2, 8, 32,  Tn  ar n1 a  2, r  4
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar  T3 T3  ar 2 T2 Tn  ar n1 Tn r Tn1 e.g.i  Find r and the general term of 2, 8, 32,  Tn  ar n1 a  2, r  4  24 n1
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar  T3 T3  ar 2 T2 Tn  ar n1 Tn r Tn1 e.g.i  Find r and the general term of 2, 8, 32,  Tn  ar n1 a  2, r  4  24 n1  22  2 n 1  22  2 n2
  • Geometric Series An geometric series is a sequence of numbers in which each term after the first is found by multiplying a constant amount to the previous term. The constant amount is called the common ratio, symbolised, r. T T1  a r 2 a T2  ar  T3 T3  ar 2 T2 Tn  ar n1 Tn r Tn1 e.g.i  Find r and the general term of 2, 8, 32,  Tn  ar n1 a  2, r  4  24 n1  22  2 n 1 Tn  22 n1  22  2 n2
  • ii  If T2  7 and T4  49, find r
  • ii  If T2  7 and T4  49, find r ar  7
  • ii  If T2  7 and T4  49, find r ar  7 ar 3  49
  • ii  If T2  7 and T4  49, find r ar  7 ar 3  49 r2  7
  • ii  If T2  7 and T4  49, find r ar  7 ar 3  49 r2  7 r 7
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. ar 3  49 r2  7 r 7
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. ar 3  49 a  1, r  4 r2  7 r 7
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. Tn  14 n1 ar 3  49 a  1, r  4 r2  7 r 7
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. Tn  14 n1 ar 3  49 a  1, r  4 r2  7 Tn  500 r 7
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. Tn  14 n1 ar 3  49 a  1, r  4 r2  7 Tn  500 r 7 4n1  500
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. Tn  14 n1 ar 3  49 a  1, r  4 r2  7 Tn  500 r 7 4n1  500 log 4n1  log 500
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. Tn  14 n1 ar 3  49 a  1, r  4 r2  7 Tn  500 r 7 4n1  500 log 4n1  log 500 n  1log 4  log 500
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. Tn  14 n1 ar 3  49 a  1, r  4 r2  7 Tn  500 r 7 4n1  500 log 4n1  log 500 n  1log 4  log 500 n  1  4.48 n  5.48
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. Tn  14 n1 ar 3  49 a  1, r  4 r2  7 Tn  500 r 7 4n1  500 log 4n1  log 500 n  1log 4  log 500 n  1  4.48 n  5.48 T6  1024, is the first term  500
  • ii  If T2  7 and T4  49, find r (iii) find the first term of 1, 4, 16, … to ar  7 be greater than 500. Tn  14 n1 ar 3  49 a  1, r  4 r2  7 Tn  500 r 7 4n1  500 log 4n1  log 500 n  1log 4  log 500 n  1  4.48 n  5.48 T6  1024, is the first term  500 Exercise 6E; 1be, 2cf, 3ad, 5ac, 6c, 8bd, 9ac, 10ac, 15, 17, 18ab, 20a