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Geometric Sequences

Geometric Sequences. Overview. Finding a geometric rule. Finding a specific term eg t 5. Finding the first term ‘a’. Finding the common ratio ‘r’. Finding the term number ‘n’. Application problems 1 2 3. Start. Geometric Sequences. Common Difference. 6, 8, 10, 12….

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Geometric Sequences

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  1. Geometric Sequences Overview. Finding a geometric rule. Finding a specific term eg t5 Finding the first term ‘a’ Finding the common ratio ‘r’ Finding the term number ‘n’ Application problems 123

  2. Start Geometric Sequences Common Difference 6, 8, 10, 12… 3, 6, 12, 24… 1, 5, 25, 125… Common Ratio 18, 15, 12, 9,… Group these sequences according to type Geometric sequences Arithmetic sequences

  3. x2 x2 x2 -3 -3 -3 Start Geometric Sequences Common Ratio Common Difference 3, 6, 12, 24… 18, 15, 12, 9,… 1, 5, 25, 125… 6, 8, 10, 12… Geometric sequences Arithmetic sequences

  4. x2 x2 x2 Start Geometric Rule tn = 3, 6, 12, 24, • n tn • 3 • 6 • 12 • 24 Common Ratio r = 2 = a (first term) = a x r0 = a x r1 = a x r = a x r x r = a x r2 = a x r x r x r = a x r3

  5. r = common ratio r = term 2 term 1 Start 1) 6, 12, 24, 48... 2) -405, 135, -45, 15... a = 6 a = -405 Find the rule which generates these sequences Geometric Example A General Rule: a = first term

  6. General Rule: Remember the power is only on the 5 Start General Rule: 6, 30, 150, 750... Find t10 Find ‘a’ a = 6 Finding a ‘Term’ Find ‘r’ Find the 10th term by substituting in a = 6 and r = 5

  7. Substitute in n = 6, t6 = 972 & r = 3 Rearrange the equation to find ‘a’ a = 4 Start Finding the first term ‘a’ Find the first term given a geometric sequence t6= 972, and a common ratio r = 3

  8. Substitute in n = 8, t8 = 10935 & a = 5 Rearrange the equation to find ‘r’ Divide by 5 Take the 7th root Start Finding the common ratio ‘r’ Find the common ratio ‘r’ given a geometric sequence with t8= 10935, and a first term of 5

  9. Substitute in r = 2, tn = 57344 & a = 14 Rearrange the equation to find ‘n’ Divide by 14 Use Logs to find n Start Finding the term number ‘n’ Find which term of a geometric sequence is equal to 57 344 (given a first term of 14, & common ratio of 2 )

  10. An Application Problem A First term = 0.8 km So a = 0.8 A 20% increase means multiply by 1.2 So r = 1.2 n = day number Start Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0.8km. Each day she has to increase her flight distance by 20% (as children become harder to find) 1) Write a rule for the flight distance on any given day

  11. Start An Application Problem B Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0.8km. Each day she has to increase her flight distance by 20% (as children become harder to find) 2) How far did Badjelly fly on the 26th day? substitute in r = 1.2

  12. Start An Application Problem C Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0.8km. Each day she has to increase her flight distance by 20% (as children become harder to find) Always Round Up! 3) The maximum flight possible on her current broomstick is 130km. when will she first fly this distance? Substitute in a = 0.8 tn = 130 r = 1.2 Term formula

  13. The characters in this PowerPoint are purely fictional and are not based on any real people either living or dead. Any coincidental resemblance to JW is unintentional and accidental.

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