找五角数的规律的方法有:a2-a1=5-1=4,a3-a2=12-5=7,a4-a3=22-12=10,…,由此可知数列{an+1-an}构成以4为首项,以3为公差的等差数列。所以an+1-an=4+3(n-1)=3n+1。a2-a1=3×1+1a3-a2=3×2+1…an-an-1=3(n-1)+1累加得:an-a1=3(1+2+….)
时间: 2024-11-14 06:32:51
找五角数的规律的方法有:a2-a1=5-1=4,a3-a2=12-5=7,a4-a3=22-12=10,…,由此可知数列{an+1-an}构成以4为首项,以3为公差的等差数列。所以an+1-an=4+3(n-1)=3n+1。a2-a1=3×1+1a3-a2=3×2+1…an-an-1=3(n-1)+1累加得:an-a1=3(1+2+….)