# 11X1 T14 02 geometric series (2011)

Post on 27-Jun-2015

400 views

Embed Size (px)

TRANSCRIPT

<ul><li> 1. Geometric Series</li></ul>
<p> 2. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm. 3. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r. 4. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.Tr 2 a 5. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.Tr 2 a T 3 T2 6. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.Tr 2 a T 3 T2Tn r Tn1 7. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.TT1 ar 2 a T 3 T2Tn r Tn1 8. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.TT1 ar 2 a T2 ar T 3 T2Tn r Tn1 9. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.TT1 ar 2 a T2 ar T3T3 ar 2 T2Tn r Tn1 10. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.TT1 ar 2 a T2 ar T3T3 ar 2 T2Tn ar n1Tn r Tn1 11. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.T T1 ar 2 aT2 ar T3 T3 ar 2 T2 Tn ar n1Tn r Tn1e.g.i Find r and the general term of 2, 8, 32, 12. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.T T1 ar 2 aT2 ar T3 T3 ar 2 T2 Tn ar n1Tn r Tn1e.g.i Find r and the general term of 2, 8, 32, a 2, r 4 13. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.T T1 ar 2 aT2 ar T3 T3 ar 2 T2 Tn ar n1Tn r Tn1e.g.i Find r and the general term of 2, 8, 32, Tn ar n1 a 2, r 4 14. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.T T1 ar 2 aT2 ar T3 T3 ar 2 T2 Tn ar n1Tn r Tn1e.g.i Find r and the general term of 2, 8, 32, Tn ar n1 a 2, r 4 24 n1 15. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.T T1 ar 2 aT2 ar T3 T3 ar 2 T2 Tn ar n1Tn r Tn1e.g.i Find r and the general term of 2, 8, 32, Tn ar n1 a 2, r 4 24 n1 22 2 n 1 22 2 n2 16. Geometric SeriesAn geometric series is a sequence of numbers in which each term afterthe first is found by multiplying a constant amount to the previousterm.The constant amount is called the common ratio, symbolised, r.T T1 ar 2 aT2 ar T3 T3 ar 2 T2 Tn ar n1Tn r Tn1e.g.i Find r and the general term of 2, 8, 32, Tn ar n1 a 2, r 4 24 n1 22 2 n 1 Tn 22 n1 22 2 n2 17. ii If T2 7 and T4 49, find r 18. ii If T2 7 and T4 49, find r ar 7 19. ii If T2 7 and T4 49, find r ar 7ar 3 49 20. ii If T2 7 and T4 49, find r ar 7ar 3 49r2 7 21. ii If T2 7 and T4 49, find r ar 7ar 3 49r2 7 r 7 22. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.ar 3 49 r2 7r 7 23. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.ar 3 49a 1, r 4 r2 7r 7 24. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.Tn 14 n1ar 3 49a 1, r 4 r2 7r 7 25. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.Tn 14 n1ar 3 49a 1, r 4 r2 7 Tn 500r 7 26. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.Tn 14 n1ar 3 49a 1, r 4 r2 7 Tn 500r 7 4n1 500 27. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.Tn 14 n1ar 3 49a 1, r 4 r2 7 Tn 500r 7 4n1 500log 4n1 log 500 28. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.Tn 14 n1ar 3 49a 1, r 4 r2 7 Tn 500r 7 4n1 500log 4n1 log 500 n 1log 4 log 500 29. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.Tn 14 n1ar 3 49a 1, r 4 r2 7 Tn 500r 7 4n1 500log 4n1 log 500 n 1log 4 log 500 n 1 4.48n 5.48 30. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.Tn 14 n1ar 3 49a 1, r 4 r2 7 Tn 500r 7 4n1 500log 4n1 log 500 n 1log 4 log 500 n 1 4.48n 5.48 T6 1024, is the first term 500 31. ii If T2 7 and T4 49, find r (iii) find the first term of 1, 4, 16, to ar 7be greater than 500.Tn 14 n1ar 3 49a 1, r 4 r2 7 Tn 500r 7 4n1 500log 4n1 log 500 n 1log 4 log 500 n 1 4.48n 5.48 T6 1024, is the first term 500Exercise 6E; 1be, 2cf, 3ad, 5ac, 6c, 8bd, 9ac, 10ac, 15, 17, 18ab, 20a</p>