Sequence Problem Detailed Process, Number Sequence Problem, Find Detailed Process

The second question is to bring in the general formula of the previous question, I can't do it, the first question is to convert all the known conditions he gave into the form of a1 + several d, for example, the first formula: a1 + a3 + a5 + a7 + a9 = 15, we can convert it into a1 + a1 + 2d + a1 + 4d + a1 + 6d + a1 + 8d = 15 according to this form to convert the second formula, connect these two formulas to calculate the first term a1 and the tolerance d, and then according to an=a1+(n-1)d brings in the a1 and d that I just calculated, and the general formula comes out. If there is a formula in the SN book, A1 and D are also used to calculate.

I hope it's really troublesome for Apple input method to play this, I hope it helps.

I just read the problem again and there is a second solution, let me improve it, use the middle term of the equal difference to calculate, you see the first formula a1 + a3 + a5 + a7 + a9 = 15. a1 + a9 constitute the middle term of the equal difference, and the sum of the two is actually equal to 2 times the a5. A3+A7 is the same thing.

Finally, the first equation is reduced to 5 times a5=15, a5=3, and the second equation is the same, and finally the first term and tolerance are calculated using the general term formula (which is available in the book). The second method is a little more technical and the steps are not much different. It is recommended that you use the second method.

This kind of fill-in-the-blank question, if the number is small, can be calculated step by step. If the number is large, you can find the equation of the difference series for calculation.

1.Geometric progression.

a1*a10=a2*a9=a3*a8=a4*a7=a5*a6=9log3(a1)+log3(a2)+…log3(a9)+log3(a10)

log3(a1*a2*……a9*a10)=log3(9^5)

log3(3^10)

2.Let the three numbers be 2-d 2 2+d d≠02, 2-d 2+d in proportional sequences.

2-d)^2=2(2+d)

4-4d+d^2=4+2d

d 2=6d d = 6 These three numbers are -4,2,82-d 2+d 2 in proportional sequences.

2+d)^2=2(2-d)

4+4d+d^2=4-2d

d 2=-6d d d=-6 These three numbers are 8,2,-4, so these three numbers are 8,2,-4 or -4,2,8

(1)a(n+1) -2an = ana(n+1)a(n+1) -ana(n+1)-2an =0[a(n+1)+an][a(n+1)-2an]=0 is a positive series, a(n+1)+an constant "0", so only a(n+1)-2an=0

a(n+1) an=2, which is a fixed value.

and a1 = 4, the number series is 4 as the first term, 2 is the common ratio of the proportional series an=4·2 =2

The general formula for the series is an=2

2) The question is incorrect, when n=1, b1=1 [log2(a1)log2(a0)], and a0 has no definition.

Solution:1

2a(n+1)=an

a(n+1) an=1 2, which is the fixed value.

A = 1 2 series is a proportional series with 1 2 as the first term and 1 2 as the common ratio.

The general formula for the series an=(1 2)(1 2) (n-1)=1 2 is an=1 2.

sn=b1+b2+..bn=1×2+2×2²+3×2³+.n×2ⁿ

2sn=1×2²+2×2³+.n-1)×2ⁿ+n×2^(n+1)

sn-2sn=-sn=2+2²+2³+.2ⁿ -n×2^(n+1)

2×(2ⁿ-1)/(2-1) -n×2^(n+1)=(1-n)×2^(n+1) -2

sn=(n-1)×2^(n+1) +2

2 (n+1) means 2 to the n+1st power.

1. 4/3，20/3.

2. sn-sn-1=(n+2/3)an-(n+1/3)an-1an=(n+2/3)an-(n+1/3)an-1(n-1/3)an=(n+1/3

an-1an/an-1=n+1/n-1

The result can be obtained by multiplying it cumulatively.