If the arithmetic sequence {an} satisfies A2 + S3 = 4, A3 + S5 = 12, then the value of A4 + S7 is______ ．

If the arithmetic sequence {an} satisfies A2 + S3 = 4, A3 + S5 = 12, then the value of A4 + S7 is______ ．

Because A2 + S3 = 4, A3 + S5 = 12, so a1 + D + & nbsp; 3A1 + 3D = 4A1 + 2D + 5A1 + 10d = 12, simultaneous can get A1 = 0, d = 1, so A4 + S7 = a1 + 3D + 7a1 + 21d = 8A1 + 24D = 24, so the answer is: 24

If the arithmetic sequence {an} satisfies A2 + S3 = 8, A4 + S7 = 16, then the value of A3 is

In the arithmetic sequence
S(2n-1) = (2n-1)an
So 8 = A2 + S3 = 4a2
a2 = 2
Similarly, A4 = 2
So A3 = 2

If the sequence {an} is an arithmetic sequence, A4 = 7, then S7=___ ．

∵ sequence {an} is arithmetic sequence, A4 = 7, ∵ S7 = 7 (a1 + A7) 2 = 7 × 2a42 = 7a4 = 49, so the answer is: 49

In the known arithmetic sequence an, a3a7 = - 16, A4 + A6 = 0, find the first n terms and Sn of an. I get two answers, why is there only one answer
My is Sn = n ^ 2-9n Sn = - n ^ 2 + 9N

There's a problem with the answer. You're right

In the arithmetic sequence {an}, S7 = 35, find A4

S7=(a1+a7)*7/2
because a1+a7=2*a4
so S7=(a1+a7)*7/2=2*a4*7/2=7*a4=35
a4=5
This kind of question type is quite common, the method is also quite commonly used~

The sum of the first n terms of the arithmetic sequence is SN. It is known that A3 = 12, S15 & gt; 0, S16 & lt; 0. Which of S1, S2,... SN is the largest

Let the equal difference be D, from A3 = 12, S15 > 0, S160, and d0,0

Let the sum of the first n terms of the arithmetic sequence {an} be Sn and satisfy S15 ＞ 0 and S16 ＜ 0, then when SN is the largest, n = ()
A. 6B. 7C. 8D. 9

The first eight terms of S15 = 15 (a1 + A15) 2 = 15 × 2a82 = 15a8 ＞ 0, S16 = 16 (a1 + a16) 2 = 16 (A8 + A9) 2 = 8 (A8 + A9) ＜ 0, a8 ＞ 0, A9 ＜ 0, the first eight terms of {an} arithmetic sequence are all positive numbers, and they are negative from the ninth term, when SN is the largest, n = 8, so choose: C

Let the sum of the first n terms of the arithmetic sequence {an} be Sn and satisfy S15 ＞ 0 and S16 ＜ 0, then when SN is the largest, n = ()
A. 6B. 7C. 8D. 9

The first eight terms of S15 = 15 (a1 + A15) 2 = 15 × 2a82 = 15a8 ＞ 0, S16 = 16 (a1 + a16) 2 = 16 (A8 + A9) 2 = 8 (A8 + A9) ＜ 0, a8 ＞ 0, A9 ＜ 0, the first eight terms of {an} arithmetic sequence are all positive numbers, and they are negative from the ninth term, when SN is the largest, n = 8, so choose: C

Let the sum of the first n terms of the arithmetic sequence {an} be Sn, and S15 ＞ 0, S16 ＜ 0, then s1a1, s2a2 The largest of s15a15 is ()
A. S15a15B. S9a9C. S8a8D. S1a1

The results show that S15 = 15 (a1 + A15) 2 = 15a8 ＞ 0, a8 ＞ 0. And S16 = 16 (a1 + a16) 2 = 16 (A8 + A9) 2 = 8 (A8 + A9) ＜ 0. A9 ＜ 0. So the arithmetic sequence {an} is a decreasing sequence. So A8 is the smallest of positive terms, A9 is the largest of negative terms, S8 is the largest, so & nbsp; s8a8 is the largest

It is known that the sum of the first n terms of the arithmetic sequence {an} is Sn, and A3 = 2a7, S4 = 17

a3=a1+2d,
a7=a1+6d
a3=2a7
The result of simultaneous three forms is: A1 = - 10d
S4=4a1+6d=-40d+6d=-34d=17
If d = - 1 / 2, then A1 = - 10d = 5
The general formula is an = a1 + (n-1) d = 11 / 2-N / 2
11 / 2-N / 2 > = 0, then n