Arithmetic sequence - 2, - 4, - 6 What is the general term formula of

Arithmetic sequence - 2, - 4, - 6 What is the general term formula of

-2n

How to use the accumulation method and the accumulation method in the sequence of numbers
What is accumulation and accumulation? Under what circumstances should accumulation and accumulation be used?
How to use it? It's better to give examples,

Sum by difference
Example 3: A1 = 1, an + 1 = an + 2n
According to the recurrence formula, a2-a1 = 2, a3-a2 = 22, a4-a3 = 23 an-an-1=2n-1
Add the above n-1 formulas to get
an=a1+2+22+23+24+… +2n-1=1+2+22+23+… +2n-1=2n-1
Note: the sequence of recurrence formula such as an + 1 = an + F (n) can be accumulated by difference
In particular, when f (n) is a constant, the sequence is equal difference sequence
Multiplication by quotient
In example 4, we know that A1 = 1, an = 2nan-1 (n ≥ 2) and find an
When n ≥ 2, = 22, = 23, = 24 =2n
Multiply the above n-1 expressions
an=a1.22+3+4+… +n=2
When n = 1, A1 = 1 satisfies the above equation
So an = 2 (n ∈ n *)
Note: the general term formula can be obtained by quotient superposition multiplication for the sequence of recurrence formula such as an + 1An = g (n). In particular, when G (n) is constant, the sequence is equal ratio sequence
There are still a few places that you can't turn around. You can go and have a look. They are all series topics

How to prove this sequence with accumulation
There must be a process!
A1 = 1, an = 3 (n-1 power of 3) + a (n-1) (n-1 is subscript) prove that an = (n-1 power of 3) / 2

A1 = 1, an = 3 ^ (n-1) + a (n-1) prove an = (3 ^ n-1) / 2 prove an = 3 ^ (n-1) + a (n-1) when n = 1, A1 = 1 = (3 ^ 1-1) / 2 when n = 2, A2 = 3 + A1 = 3 + (3 ^ 1-1) / 2 = (3 ^ 2-1) / 2 when n = 3, A3 = 3 ^ 2 + A2 = 3 ^ 2 + (3 ^ 2-1) / 2 = (3 ^ 3-1) / 2 when n = 3 When n = n-2, a (n-2) =