High School Mathematics Equal Difference Sequence Lesson Plans

Equal difference series'The general formula is: an=a1+(n-1)d

or an=am+(n-m)d

The first n terms and formulas are: sn=na1+[n(n-1)2] d or sn=(a1+an)n2

If m+n=2p, then: am+an=2ap

The above n are positive integers.

Text translation. The value of the nth term = first term + (number of items - 1) * tolerance.

The sum of the first n terms = (first term + last term) * number of terms 2

Tolerance = Later Term - Previous Term.

Equation for summing proportional sequences.

1) Proportional series: a (n+1) an=q (n n).

2) General formula: an=a1 q (n-1); Promotional: an=am q (n-m);

3) Summing formula: sn=n a1 (q=1) sn=a1(1-q n) (1-q) =a1-an q) (1-q) (q≠1) (q is the common ratio, n is the number of terms).

4) Properties: If m, n, p, q n, and m+n=p+q, then am an=ap aq;

In a proportional sequence, the sum of each k terms remains in proportional sequence.

If m, n, q n, and m+n=2q, then am an=aq 2

5)"g is the proportional middle term of a and b""g^2=ab(g ≠ 0)".

6) In the proportional series, neither the first term A1 nor the common ratio q are zero. Note: In the above formula, an denotes the nth term of the proportional series.

Derivation of the summation formula for proportional sequences: sn=a1+a2+a3+.an(common ratio is q) q*sn=a1*q+a2*q+a3*q+..

an*q =a2+a3+a4+..a(n+1) sn-q*sn=a1-a(n+1) (1-q)sn=a1-a1*q^n sn=(a1-a1*q^n)/(1-q) sn=(a1-an*q)/(1-q) sn=a1(1-q^n)/(1-q) sn=k*(1-q^n)~y=k*(1-a^x)。

Because (an) is a series of equal differences, s10, s20-s10, s30-s20....S100-S90, S110-S100 are also equal difference series, and tolerance D is 100 times that of AN. (i.e. d=100d).

s100=s100-s90+..s20-s10+s10=s10+s10+d+s10+2d+..s10+9d=10*s10+45d

d=(s100-10*s10)/45=(10-10*100)/45=-22

s110=s110-s100+s100-s90+..s20-s10+s10=s10+s10+d+s10+2d+..s10+9d+s10+10d=11s10+55d=11*100-55*22=-110