In the sequence (an), A1 = - 18, an + 1 (n + 1 in the lower right corner of a) = an + 3, n ∈ n +, then the first few terms of the sequence (an) and the minimum value of Sn are?

In the sequence (an), A1 = - 18, an + 1 (n + 1 in the lower right corner of a) = an + 3, n ∈ n +, then the first few terms of the sequence (an) and the minimum value of Sn are?

Because an + 1-an = 3
So {an} is an arithmetic sequence
So an = - 18 + (n-1) × 3 = = 3n-21
Because d = 3 > O, the arithmetic sequence is an increasing sequence
Because A6 = - 3 < 0, a7 = 0
So S6 or S7 is the smallest

The sequence {an} satisfies A1 = 1. A (n + 1) √ {1 / (an) 2 + 4} = 1. Note Sn = A12 + A22 +. S (2n-1) - Sn ≤ M / 30, and find the minimum value of positive integer M
The square of A1 is 2
Sn=a12+a22+，，，，，+an2
S (2n-1) - Sn ≤ M / 30
Now I can find {1 / an2} arithmetic, an2 = 1 / (4n-3)

S (2n + 1) - Sn ≤ M / 30? ∵ sequence {a [n]} satisfies a [n + 1] √ (1 / a [n] ^ 2 + 4) = 1 ∵ 1 / a [n + 1] ^ 2-1 / a [n] ^ 2 = 4 ∵ a [1] = 1 ∵ 1 / a [n] ^ 2} is an arithmetic sequence with the first term of 1 / a [1] ^ 2 = 1 and tolerance of 4, that is: 1 / a [n] ^ 2 = 1 + 4 (n-1) = 4n-3 ∵ a [n] ^ 2 = 1 / (4n-3) ∵ s [n] = a [1