Let the sum of the first n terms of the arithmetic sequence {an} be Sn, where A6 = 13 and S10 = 20 Finding the general term formula of sequence {an} If the sequence {BN} satisfies BN = 2 / an * an + 1 (n ∈ n *), find the first n terms and TN of the sequence {BN}

Let the sum of the first n terms of the arithmetic sequence {an} be Sn, where A6 = 13 and S10 = 20 Finding the general term formula of sequence {an} If the sequence {BN} satisfies BN = 2 / an * an + 1 (n ∈ n *), find the first n terms and TN of the sequence {BN}

∵ the sum of the first n terms of {a [n]} is s [n], a [6] = 13, s [10] = 20 ∵ a [6] = a [1] + 5D = 13s [10] = 10A [1] + 45d = 10. The solution is: a [1] = - 107, d = 24 ∵ a [n] = - 107 + 24 (n-1), that is: a [n] = 24n-131 ∵ sequence {B [n]} satisfies B [n] = 2 / (a [n] a [n + 1]) (n ∈ n *} B [n] = 2 / [(24n-131}

If A5 = 20-a6, then S10 =?

Because A5 = 20-a6
So A5 + A6 = 20
So 2A1 + 9D = 20
S10=0.5n（a1+a10）=5（2a1+9d）=100

Given that the sum of the first n terms of the arithmetic sequence {an} is Sn, and S10 = 12, then A5 + A6 = ()
A. 125B. 12C. 6D. 65

From the summation formula of arithmetic sequence, we can get: S10 = 10 (a1 + A10) 2 = 12, we can get a1 + A10 = 125, and from the properties of arithmetic sequence, we can get: A5 + A6 = a1 + A10 = 125, so we choose a

It is known that the tolerance of the arithmetic sequence an is not zero, and the sum of the first n terms is SN. If A1, A4 and A5 are equal ratio sequence, and S6 = 5a3-1 (5 times A3 minus 1), (1) find the general term formula, (2) when n is taken, the maximum value of Sn is taken? Find the maximum value^_ ^)

(1)
a4=a1+3d,a5=a1+4d
Because A1, A4, A5 are equal ratio sequences
So A4 ^ 2 = A1 * A5
That is, (a1 + 3D) ^ 2 = A1 * (a1 + 4D)
So 2A1 * D + 9D ^ 2 = 0
Because D ≠ 0
So 2A1 + 9D = 0
S6 = 5a3-1
S6=6(a1+a6)/2=3(a1+a6)=3(a1+a1+5d)=6a1+15d
5a3-1=5(a1+2d)-1=5a1+10d-1
So 6A1 + 15d = 5A1 + 10d-1
That is a1 + 5D + 1 = 0, ②
At the same time, a 1 = 9, d = - 2
So an = a1 + (n-1) d = 9-2 (n-1) = 11-2n
(2)
Sn=n(a1+an)/2=n(9+11-2n)/2=n(10-n)
The symmetry axis of Sn is n = 10 / 2 = 5, so when n = 5, the maximum value of Sn is S5 = 5 * (10-5) = 25

The tolerance of the arithmetic sequence {an} is not zero, and the first term A1 = - 12. If A1, A3, A4 and A5 form an arithmetic sequence, find the minimum value of the first n terms and Sn

a1*a5=a3*a4
a1*(a1+4d)=(a1+2d)(a1+3d)
d = 2
The smallest SN is an

It is known that the sequence {an} (n ∈ n *) is an arithmetic sequence with the first term of 1, and its tolerance D ＞ 0, and A3, a7 + 2 and 3a9 are equal proportion sequences. (1) find the general term formula of the sequence {an}; (2) let the sum of the first n terms of the sequence {an} be Sn, and find the maximum value of F (n) = Sn (n + 18) Sn + 1

(1) ∵ A3, a7 + 2, 3a9 are equal proportion sequence ∵ (A7 + 2) 2 = A3 · 3a9, that is: (a1 + 6D + 2) 2 = (a1 + 2D) · 3 (a1 + 8D) solution: D = 1 ∵ an = n; (2) from (1) Sn = n (n + 1) 2 ∵ f (n) = n (n + 1) 2 (n + 18) · (n + 1) (n + 2) 2 = n (n + 18) (n + 2) = 1n + 36N + 20 ≤ 132 ∵ f (n) ∵ (a1 + 6D + 2) 2 = (a1 + 2D) · 3

It is known that the sequence {an} is an arithmetic sequence with tolerance 2, and a1 + 1, A3 + 1, a7 + 1 are equal ratio sequence. Find the general term of {an}
The known sequence {an} is an arithmetic sequence with tolerance 2, and a1 + 1, A3 + 1 and A7 + 1 are equal proportion sequences
Find the general term formula of {an}

An is the arithmetic sequence of D = 2,
that
a1=a1、a3=a1+4、a7=a1+12
Because a1 + 1, A3 + 1, a7 + 1 are equal ratio sequences,
that
(a1+1)(a7+1)=(a3+1)(a3+1)
thus
(a1+1)(a1+13)=(a1+5)(a1+5)
therefore
a1a1+14a1+13=a1a1+10a1+25
4a1=12
a1=3
So the general formula is: an = 3 + (n-1) × 2 = 2n + 1
[Economic Mathematics team answers for you!]

Given that Sn in the arithmetic sequence {an} is the sum of the first n terms, and A2 = 6, a7 = - 4, find A1 and S10

A2=6,A7=-4,
A7-A2=5d=-4-6=-10
d=-2
an=a1+d(n-1)
6=A1-2*1
A1=8
A10=8-2*(10-1)=-10
S10=(8-10)*10/2=-10

In the arithmetic sequence {an}, (1) given Sn = 2n ^ 2-3n, find an sum D (2) A2 = 3, a7 = 13, find S10
What about D

a1=-1,d=4;
a1=1,d=2,s10=100

The known sequence an is an arithmetic sequence, the sum of the first n terms is Sn, A2 = 4, S10 = 145
①a2+a4+a8…… +a2^n②2a1+4a2+8a3+…… +2^nan

A2 = a1 + D = 4s10 = 10A1 + 45d = 10A1 + 10d + 35d = 10 (a1 + D) + 35d = 40 + 35d = 14535d = 105d = 3A1 = a2-d = 4-D = 4-3 = 1 sequence {an} is an arithmetic sequence with 1 as the first term and 3 as the tolerance. An = 1 + 3 (n-1) = 3n-2 ① A2 + A4 + A8 +... + a (2 ^ n) = a1 + 2d-d + A1 + 4d-d + A1 + 8d-d +... + A1 + (2 ^ n) d-d