It is known that the sum of the first three terms of the arithmetic sequence {an} is - 3, and the product of the first three terms is 8 (1) The general term formula of {an} (2) A3 & # 178; = a2a1, find the sum of the first n terms of the sequence {| a}

It is known that the sum of the first three terms of the arithmetic sequence {an} is - 3, and the product of the first three terms is 8 (1) The general term formula of {an} (2) A3 & # 178; = a2a1, find the sum of the first n terms of the sequence {| a}

(1) If the sum of the first three terms of the arithmetic sequence {an} is - 3, then A2 = - 3 △ 3 = - 1
Let the tolerance of sequence be D, the first three terms be - 1-D, - 1, - 1 + D, and the product be 8. If (- 1-D) × (- 1) × (- 1 + D) = 8, we can get D & # 178; = 9, and we can see that d = 3 or D = - 3. Thus, the first three terms are: - 4, - 1,2 or 2, - 1, - 4
It can be seen that the general formula of {an} is: an = - 4 + (n-1) × 3 = 3N-7 or an = 2 + (n-1) × (- 3) = - 3N + 5
(2) If A3 & # 178; = a2a1, then A2, A3 and A1 form an equal ratio sequence. From the above conclusion, we know that d = 3,
The general formula of {an} is: | an | = | 3N-7 |
Because an arithmetic sequence has at least three terms, the sum of the first n terms of the sequence {an} is:
Sn=4+1+（n-2）（2+3n-7）÷2=[（3n-5）（n-2）/2]+5

If the first three terms of the arithmetic sequence {an} are X-1, x + 1, 2x + 3, then the general term formula of the sequence is ()
A. an=2n-5B. an=2n-3C. an=2n-1D. an=2n+1

The first three terms of ∵ arithmetic sequence {an} are X-1, x + 1, 2x + 3, ∵ (x + 1) - (x-1) = (2x + 3) - (x + 1), and the solution is x = 0. ∵ A1 = - 1, d = 2, an = - 1 + (n-1) × 2 = 2n-3

Is the general term formula of two arithmetic sequences an arithmetic sequence after addition or subtraction

an=a1+(n-1)d1
bn=b1+(n-1)d2
So an + BN = (a1 + B1) + (n-1) (D1 + D2)
So it's an arithmetic sequence, the first term is a1 + B1, tolerance D1 + D2
In the same way
An BN is also an arithmetic sequence