Formula for the nth term of a Geometric sequence. an a rn-1 where an is the nth term a, is the first term r is the common ratio n is the number of termsHow do we get the nth term of a sequence using the formula? Example 1: Find the 8"h term of the geometric sequence 24, 12, 6, a8 =?;n = 8; a1 = 24;?" = 1/2 an = earn1 as = 24[(1/2)8'1] a8 = 24(1/2)7 a8 = 24(1/128) \"18 = 3/16 .FTL _J $ I. f \\- 0 .- \\ up ' - \\ How do we get the 1st term of a sequence using the formula? Solution: a1 =?; n = 4; an = -40;1 = -2 an = arn-1 -40 = a1 (-2)4-1 -40 = a1 (-2)3 -40 = -801 a1 = 5Alternative solution to find the common ratio Formula:r = n-k an ak where a, is the farthest term of the sequence and a is the nearest termHow do we get the common ratio using the alternative formula? n-k an r= ak 11-7 480 r = 30 r = 4v16 r = +2GEOMETRIC SERIES A geometric series is the indicated sum of the terms of a geometric sequence. To find the sum of the geometric sequence the a1(1rn) 11" formula Sn = can be used. \fIllustrative Examples: 1. Find the sum of the first 1 2 terms of the geometric sequence 3, -9, 27, -81, 243, Solution: n = 12; a1= 3 r=-3 S _ 611(1Tn) 1 r 3(1 - (-3)12) 1 (3) _ 3(1 531441) 1+3 512 = 512 _ 3(531440) 512 _ 4 = 398, 580 A ctivity 2: Find the indicated term of the geometric sequence and the series with the given sequences. 3, 9 27, 81,...;a9;59 9 27 2 37:: ...;a10;.5'10 1, 0.1 0.,01 0.001,...;a8;58 -}a7;57 jag); S6