1. The first n terms of a sequence and Sn = an ^ 2 + BN + C (a is not equal to 0) Ask (1) the formula an of the sequence; (2) whether the sequence constitutes the arithmetic sequence? 2. It is known that the sum of the first n terms of the sequence {an} is Sn and satisfies A1 = 1 / 2, an + 2snsn-1 = 0 (n > = 2) (1) Judge whether {1 / Sn} is arithmetic sequence and prove that (2) find Sn and an 3. In the natural number set y = f (x), we know that when x = 1, f (x) + F (x + 1) = 5, when x is odd, f (x + 1) - f (x) = 1, when x is even, f (x + 1) - f (3) = 3 (1) Verification: F (1), f (3), f (5) F (2n-1) (n ∈ n) is an arithmetic sequence; (2) Find the analytic expression of: F (x) thx! The third question should be: If x is odd, f (x + 1) - f (x) = 1; if x is even, f (x + 1) - f (x) = 3, and f (1) + F (2) = 5 (1) Prove f (1), f (3) F (2n-1) (n is a positive integer) is an arithmetic sequence (2) Finding the analytic expression of F (x)

1. The first n terms of a sequence and Sn = an ^ 2 + BN + C (a is not equal to 0) Ask (1) the formula an of the sequence; (2) whether the sequence constitutes the arithmetic sequence? 2. It is known that the sum of the first n terms of the sequence {an} is Sn and satisfies A1 = 1 / 2, an + 2snsn-1 = 0 (n > = 2) (1) Judge whether {1 / Sn} is arithmetic sequence and prove that (2) find Sn and an 3. In the natural number set y = f (x), we know that when x = 1, f (x) + F (x + 1) = 5, when x is odd, f (x + 1) - f (x) = 1, when x is even, f (x + 1) - f (3) = 3 (1) Verification: F (1), f (3), f (5) F (2n-1) (n ∈ n) is an arithmetic sequence; (2) Find the analytic expression of: F (x) thx! The third question should be: If x is odd, f (x + 1) - f (x) = 1; if x is even, f (x + 1) - f (x) = 3, and f (1) + F (2) = 5 (1) Prove f (1), f (3) F (2n-1) (n is a positive integer) is an arithmetic sequence (2) Finding the analytic expression of F (x)

First: (1): when n > = 2, an = SN-S (n-1) = an ^ 2 + BN + C-A (n-1) ^ 2-B (n-1) - C = 2an-a + BN = 1, an = Sn = a + B + C, so an = a + B + C (n = 1) = 2an-a + B (n > = 2) (2): first, test whether an = 2an-a + B when n > = 2 can be used for n = 1n = 1, A1 = a + B, obviously when C = 0, an = 2An when n > = 2

(1) There are 16 workers in a workshop who produce spectacle frames and lenses. On average, each worker can produce 50 pairs of spectacle frames or 80 pieces of lenses. How to allocate personnel to make the lenses or lenses just matched?
(2) 56 students from grade one of a junior high school were selected to participate in the soil transportation work on campus and were given 40 shoulder poles. How many people should be arranged to carry the soil and how many people should carry the soil so as to match the number of people with the number of shoulder poles

1. Set X person to produce the frame and Y person to produce the lens
X+Y=16
50X=（80÷2）Y
The answer is not an integer
2. X people carry, y people pick
X+Y=56
X/2+Y=40
X=32,Y=24

Some primary school students serve the community. The number of boys is two-thirds of the number of girls. Later, three boys joined and three girls left. At this time, the number of boys is three-quarters of the number of girls. How many boys and girls are serving the community? I have been struggling with this problem for a long time, and I am very anxious

Let the initial female X male be 2 / 3x
Lie equation
2/3x + 3=3/4（x - 3）
2/3x + 3=3/4x - 3/4* 3
2/3x - 3/4x=- 3/4* 3 - 3
x=63
Female X = 63;
Male 2 / 3x = 42;
A: there were 42 boys and 63 girls serving the community