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Kuta Software - Infinite Algebra 2 Name. Geometric Sequences Date. Period Determine if the sequence is geometric. If it is, find the common ratio. 1) -1, 6, —36, 216,... 2) -1, 1, 4, 8... r=-6 Not geometric 3) 4, 16, 36, 64,... 4) -3, -15, -75, —375, ... Not geometric r=5 5) -2, -4, -8, -16, ... 6) 1, -5, 25, -125, ... r=2 r=-5 Given the explicit formula for a geometric sequence find the first five terms and the 8th term. T = gn 1 atl First Five Terms: 1, 3, 9, 27, 81 lL. 1 a, = 2187 First Five Terms: 2, —, —, —-, —— 2 8 32 128 1 a,=—— * 8192 9) a,=-25.4""! 10) a,=-4.3""! First Five Terms: —2.5, —10, —40, —160, —640 First Five Terms: -4, —12, —36, —108, —324 a, = 40960 a, =—8748 Given the recursive formula for a geometric sequence find the common ratio, the first five terms, and the explicit formula. I) asa, .-2 -3 a,=2 Common Ratio: r=2 Common Ratio: r =—3 First Five Terms: 2, 4, 8, 16, 32 First Five Terms: —3, 9, —27, 81, —243 Explicit: 4, =2-2"~' Explicit: a, =—3 - (-3)""! 13) a,=a_.°5 14) a,=a__ +3 a,=2 a,=-3 ‘Common Ratio: r=5 Common Ratio: First Five Terms: 2, 10, 50, 250, 1250 First Five Terms: -9, -27, -81, -243 Explicit: a,=2-5"~! Explicit: 4, =-3-3"~" 
