Use the example below to answer this question: Determine whether the following are arithmetic or geometric progressions (or neither/both), then find the formula for a n , and finally find the sum of the first 10 terms:a) -7/4,-1,-1/4,1/2,....b?1,-2/3,4/9,-8/27,...c) 16, 1.6, 0.16, 0.016,...d) 9, 3, -3, -9,...

Problem 14. Arithmetic and Geometric Progressions. 20 points. Determine whether the following are arithmetic or geometric progressions (or neither), then find the formula for an, and finally find the sum of the first 12 terms: a) -3. -6. -12, -24. ... b) 1. 3. 9. 4.... c) 0.001. 0.01, 0.1, 1, ... d) 1, 1, 1, 1, ... Solution: (a) a= - 3 r=2 GEOMETRIC an = arn - 1 an = - 3( 2 ) " - 1 Su = a(1-r) SR= -3(1-2) _ = - 12 , 285 1- 2 ( 6 ) d= 2 a = t ARITHMETIC an = a + ( n-1) d an = 2 + ( n- 1) . 2 = 2n- 3 8n = 2 2a+ ( 1-1)d 512 = 12 | 2 . 2 + ( 12 - 1 ) . 2 7 = 6. 1 1 + 22 ) = 6-23 = 138 ( c ) a= 0.ool r= 10 GEOMEmic an = 0.0 01 ( 10 ) 12 - 1 Sn = 0.001(1-10(2) 1 - $20 # 10 (d) al r=1 GEOMETRIC IF r=I , THEN Sn = na S12 = 12. 1 = 12 12