Given that the sum of the first n terms of sequence {an} A1 = 2 is Sn and satisfies Sn sn-1 = 3an, the general term formula an of sequence {an} is obtained Given that the sum of the first n terms of the sequence {an} A1 = 2 is Sn and satisfies Sn + sn-1 = 3an, the general term formula an of the sequence {an} is obtained

Given that the sum of the first n terms of sequence {an} A1 = 2 is Sn and satisfies Sn sn-1 = 3an, the general term formula an of sequence {an} is obtained Given that the sum of the first n terms of the sequence {an} A1 = 2 is Sn and satisfies Sn + sn-1 = 3an, the general term formula an of the sequence {an} is obtained

Because Sn + sn-1 = 3an
So sn-1 + sn-1 + an = 3an
2Sn-1=2an
Sn-1=an
Because Sn = an + 1
So Sn - sn-1 = an + 1-an
an=an+1-an
2an=an+1
an+1/an=2
Because A1 = 2
So an = 2 ^ n (n > = 2)
2 (n=1)

Given that the sequence {an} satisfies 3 (an + 1) + an = 4 (n > = 1), and A1 = 9, the sum of the first n terms is Sn, then the inequality {sn-n-6} is satisfied

3A (n + 1) + an = 43A (n + 1) = - an + 43A (n + 1) - 3 = - an + 1 [a (n + 1) - 1] / (an - 1) = - 1 / 3, which is the constant value. A1-1 = 9-1 = 8, the sequence {an - 1} is an isometric tree with 8 as the first term and - 1 / 3 as the common ratio. An = 8 × (- 1 / 3) ^ (n-1) + 1sn = 8 × [1 - (- 1 / 3) & # 8319;] / [1 - (- 1 / 3)] + n = n + 6-6 × (- 1 / 3) & # 8

In the known sequence {an}, if A1 = 8 and 2An + 1 + an = 6, the sum of the first n terms is Sn, then the minimum positive integer n satisfying the inequality | sn-2n-4 | 12800 is ()
A. 12B. 13C. 15D. 16

2An + 1 + an = 6 {an + 1-2 = − 12 (an − 2), so {An-2} is an equal ratio sequence with the first term of 6 and the common ratio of − 12, so An-2 = 6 × (− 12) n-1, then Sn = 2n + 4-4 × (− 12) n, | sn-2n-4 = - 4 × (− 12) n. | sn-2n-4 | 12800 {12n − 2 ＜ 12800} 2n − 2 ＞ 2800, and 210 = 1024211 = 2048, so the minimum positive integer satisfying the condition is n = 13, so select B

In the known sequence {a n}, if A1 = 8 and 2A (n + 1) + an = 6, the sum of the first n terms is Sn, then the inequality | sn-2n-4 is satisfied|

The sum of the first n terms of An-2 is 4 [1 - (- 1 / 2) ^ n]
Sn=4[1-(-1/2)^n]+2n
|-4(-1/2)^n|12.97
n=13