Chapter 28： I am studying the Goldbach conjecture (1/2)

”Qin Luo, get up and talk about your process of solving this problem.” Just then, Li Wei's ”kind” words brought Qin Luo back to reality.

Let Sn be the first n items of the arithmetic sequence {an} and always a1=-7S3=-15

(1) Find the general term formula of {an}.

(2) Find Sn and find the minimum value of Sn.

This is an arithmetic minimum problem.

The first one is relatively simple, just find the general term formula, but the second one is more difficult.

Not only the value, but also its minimum value.

Teacher Li, this is to create an opportunity to make me pretend.

He is a rare teacher in a century.

At this moment, in Qin Luo's eyes, Li Wei was no longer a black-faced evil spirit, but a little white flower without sadness.

Qin Luo went to the blackboard and picked up the chalk and didn't answer immediately. He fell into deep thought.

Which method should I use to pretend?

Five minutes later, Qin Luo did not write a word, he stood in a daze at the blackboard.

”Qin Luo!” Li Wei's face was pale, he scolded, ”What are you waiting for.”

”Emmm, I'm thinking of using that method to solve it.”

”Why, do you have several methods?” Li Wei came to be interested. For the arithmetic sequence, the knowledge of high school covers a solution. He was curious about what solution Qin Luo could ”invent”.

”Not much, not much, only three.”

”...”

”The first kind.” Qin Luo raised his hand and wrote a capital one on the blackboard, and then quickly began to solve the problem.

”Suppose the tolerance of {an} is d, and from the question, 3a1+3d=-15”

From a1=-7, d=2

So the general term formula of {an} is an=2n-9

(2) Sn=n²-8n=(n-4)² in (1) So when n=4, Sn is the minimum value and the minimum value is -16

”The second kind”