Arithmetic and Geometric Seque

myteapot172000

2011-05-23 7:28 am

Find the number of integers between 1001 and 2000 which are divisable by12.

How many multiples of 7 are there between 101and 1000?

For the arithentic sequence -101,-98,-95,...,43,find
(a)the first positive term

(b)the number of positive terms

回答 (1)

螞蟻雄兵

2011-05-23 7:47 am

✔ 最佳答案

1 Find the number of integers between 1001and 2000 which are divisable by12.
Sol
1001>=12x=2000
83.41<=x<=166.66
84<=x<=166
166－84+1=83

2 How many multiples of 7 are there between 101and 1000?
Sol
101<=7x<=1000
14.42<=x<=142.85
15<=x<=142
142－15+1=128

3 For the arithentic sequence －101，－98，－95，...，43，find
(a)the first positive term
Sol
a1=－101
d=－98+101=3
ap=a1+(p－1)*d>0
－101+(p－1)*3>0
3p>104
p>34.6
p>= 35
a35=a1+34*3=－101+102=1
(b)the number of positive terms
an=a1+(n－1)*3=43
3n－104=43
n=49
49－35+1=15

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