观察下面三行数1,-2,4,-8,16,-32 …①0,-6,6,-18,30,-66 …②2,-4
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观察下面三行数
1,-2,4,-8,16,-32 …①
0,-6,6,-18,30,-66 …②
2,-4,8,-16,32,-64 …③
取每行数的第8个数,计算它们的和是______.
1,-2,4,-8,16,-32 …①
0,-6,6,-18,30,-66 …②
2,-4,8,-16,32,-64 …③
取每行数的第8个数,计算它们的和是______.
![观察下面三行数1,-2,4,-8,16,-32 …①0,-6,6,-18,30,-66 …②2,-4](/uploads/image/z/1899391-31-1.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E9%9D%A2%E4%B8%89%E8%A1%8C%E6%95%B01%EF%BC%8C-2%EF%BC%8C4%EF%BC%8C-8%EF%BC%8C16%EF%BC%8C-32%26nbsp%3B%E2%80%A6%E2%91%A00%EF%BC%8C-6%EF%BC%8C6%EF%BC%8C-18%EF%BC%8C30%EF%BC%8C-66%26nbsp%3B%E2%80%A6%E2%91%A12%EF%BC%8C-4)
观察可看出第一行的数分别是-2的0次方,一次方,二次方,三次方,四次方…且奇数项是负数,偶数项是正数,用式子表示规律为:(-2)n-1;
当n=8时,(-2)n-1=(-2)8-1=-128;
观察可知,第三行数是第一行的2倍,故第八个数为-256;第二行数是第三行相对应的数小2,故第八个数是-130,
∴-128-256-130=-642.
故答案为-642.
当n=8时,(-2)n-1=(-2)8-1=-128;
观察可知,第三行数是第一行的2倍,故第八个数为-256;第二行数是第三行相对应的数小2,故第八个数是-130,
∴-128-256-130=-642.
故答案为-642.
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