[high school sequence] do you know that three consecutive terms can be used to find the general formula of the sequence In the stem of the question, I only said that this is a sequence of positive numbers, and I also gave a formula. The first question is to find a1a2a3, and the second question is to find the general term formula. I derived A1, A2, A3. Can I use a3-a2 = a2-a1 = D or A3 / A2 = A2 / A1 = q to find the general term formula? Or should I use the formula given by the stem of the question to prove it? Although I have made the correct answer in both methods. The question is a little long. No point. Who will answer, It is known that {an} is a sequence of positive numbers, and the median of the equal difference between an and 2 is equal to the median of the equal ratio between Sn and 2. I calculate A1 = 2, A2 = 6, A3 = 10, Then the second question can be directly explained as arithmetic sequence according to a3-a2 = a2-a1 = D? How to answer the questions in the exam? I feel too confused and want to close this question

[high school sequence] do you know that three consecutive terms can be used to find the general formula of the sequence In the stem of the question, I only said that this is a sequence of positive numbers, and I also gave a formula. The first question is to find a1a2a3, and the second question is to find the general term formula. I derived A1, A2, A3. Can I use a3-a2 = a2-a1 = D or A3 / A2 = A2 / A1 = q to find the general term formula? Or should I use the formula given by the stem of the question to prove it? Although I have made the correct answer in both methods. The question is a little long. No point. Who will answer, It is known that {an} is a sequence of positive numbers, and the median of the equal difference between an and 2 is equal to the median of the equal ratio between Sn and 2. I calculate A1 = 2, A2 = 6, A3 = 10, Then the second question can be directly explained as arithmetic sequence according to a3-a2 = a2-a1 = D? How to answer the questions in the exam? I feel too confused and want to close this question

If you want to use them, first you need to prove that they are arithmetic or proportional series, and then you can use them. It's impossible to use them directly
It's OK to use the formula in the title, as long as the middle steps are right
There is no conflict between the two methods
You can use it
This is mainly because, in the examination room, you can think of which one to use, not which one to use

Sum of quadratic sequence
1^2+2^2+3^2+4^2+…… +What is n ^ 2 equal to? Give the derivation process, don't copy Three times launched don't It's better to give the idea of pushing

In the method of undetermined coefficient, if the summation of arithmetic sequence can be conjectured that the summation of first-order sequence becomes quadratic, then the summation of second-order sequence will be cubic, so we can set Sn = an ^ 3 + BN ^ 2 + CN + D, make n be 1,2,3,4 respectively, and solve a, B, C, D to get SN

How to find 1, 111, 111.2, 222.. n, NN, NNN, nnnn for such a series
The general method of solving the problem

a1=1=1×10^0
a2=11=1×(10^0+10^1)
a3=111=1×(10^0+10^1+10^2)
.…………
an=1×[10^0+10^1+10^2+...+10^(n-1)]=(10^n-1)/(10-1)=(10^n-1)/9
2,3,4,…… It's the same time, but the front is 2, 3, 4
When it's n:
an=n(10^n-1)/9