Geometric Sequences Overview Finding a geometric rule Finding

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 6, 8, 10, 12… 1, 5, 25, 125… 3, 6, 12, 24… 18, 15, 12, 9, … Group these sequences according to type Arithmetic sequences Geometric sequences

Start Geometric Sequences Common Difference -3 -3 -3 18, 15, 12, 9, … 6, 8, 10, 12… Arithmetic sequences Common Ratio x 2 x 2 3, 6, 12, 24… 1, 5, 25, 125… Geometric sequences

Start Geometric Rule tn = 3, 6, 12, 24, n tn Common Ratio r = 2 1 3 = a (first term) = a x r 0 2 6 3 12 x 2 =axrxr x 2 4 24 = a x r x r = a x r 1 = a x r 2 = a x r 3

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

Finding a Term Start 6, 30, 150, 750. . . Find t 10 Find General Rule: a=6 ‘a’ Find ‘r’ General Rule: Find the 10 th term by substituting in a = 6 and r = 5 Remember the power is only on the 5

Start Finding the first term ‘a’ Find the first term given a geometric sequence t 6 = 972, and a common ratio r = 3 Substitute in n = 6, t 6 = 972 & r = 3 Rearrange the equation to find ‘a’ a=4

Start Finding the common ratio ‘r’ Find the common ratio ‘r’ given a geometric sequence with t 8 = 10935, and a first term of 5 Substitute in n = 8, t 8 = 10935 & a = 5 Rearrange the equation to find ‘r’ Divide by 5 Take the 7 th root

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 ) Substitute in r = 2, tn = 57344 & a = 14 Rearrange the equation to find ‘n’ Divide by 14 Use Logs to find n

Start An Application Problem Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0. 8 km. 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 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 An Application Problem Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0. 8 km. 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 26 th day? substitute in r = 1. 2

Start An Application Problem Badjelly the witch catches children while flying her broomstick. On day 1 she flies 0. 8 km. Each day she has to increase her flight distance by 20% (as children become harder to find) 3) The maximum flight possible on her current broomstick is 130 km. when will she first fly this distance? Substitute in a = 0. 8 Always tn = 190 r = 1. 2 Term formula Round Up!

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