標題:
Math(geometric sequence)
發問:
1.Express the following recurring decimals as fractions. 0.16 (6上面有點) 2.The 2nd term and the 3rd term of a geometric sequence are 56 and 32 respectively. (a)Find the common ratio of the geometric sequence. 3.It is given that 6 , k ,3k/4 form a geometric dequence. (a)Find the value of k.
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最佳解答:
1. 0.6+0.06+0.006+... -0.5 2. ar=56 ----- (1) ar^2=32 ------ (2) (2)/(1) , r=32/56 = 4/7 common ratio = 4/7 3. k / 6 = 3k/4 / k 4k=18 k=9/2 = 4.5
其他解答:
1) Let x=0.166666666666......(1) then 10x=1.66666666..........(2) (2)-(1): 9x= 1.5=3/2 ............x=1/6 2a) common ratio=32/56=4/7 3a) Since 6,k,3k/4 form a G.S., therefore k/6= (3k/4)/k k/6=3/4 k=9/2|||||1:Let x be 0.16(6上面有點) x=0.166666666666666666........ 10x=1.666666666666............. 100x=16.66666666666............ 100x-10x=16.666666........- 1.6666666666............. 90x=15 x=15/90(15分之90) 2.56:32=28:16=14:8=7:4 3.(no relatinship)
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