Let the number in the middle of the first line be a 1= 1, the number in the middle of the second line be a2=3, the number in the middle of the third line be A3 = 7 ... the number in the middle of the sixth line be A6 = 3 1 ... the number in the middle of the nth line is an, and the number in the middle of the N- 1 line is an.

Differences between two adjacent projects:

A2-a1= 3-1= 2 = 2 *1Description: Observe the product of the last equal sign by induction.

a3-a2=7-3=4=2*2

a4-a3= 13-7=6=2*3

……

a(n- 1)-a(n-2)=2*(n-2)

An-a(n- 1)=2*(n- 1) Description: According to the above rules, it can be summarized, which is also a test of students' mathematical observation ability!

The above formula is increased accordingly:

an-a 1 = 2 * 1+2 * 2+2 * 3+……+2 *(n- 1)

= 2 * (1+2+...+(n- 1)) Description: Select the same item 2 on the right.

=2* (n*(n- 1)/2) The sum of numbers (n- 1+2+...+(n- 1) is in brackets.

=n*(n- 1)

Therefore, an = a1+n * (n-1) =1+n * (n-1) = n 2-n+1shift the term to get the final result.

This problem should be a moderately difficult one for junior two students, which mainly examines the ability of mathematical observation and induction.

The above is the process of thinking and explaining to you. I hope I can help you and look forward to your affirmation.