Let the first term of the arithmetic sequence {an} be A1, the tolerance be D, and Sn be the sum of its first n terms. If a11 = 0, S14 = 98 (1), the general term formula of {an} can be obtained (2) Under the condition of (1), find the first n terms and TN of the sequence {an}

Let the first term of the arithmetic sequence {an} be A1, the tolerance be D, and Sn be the sum of its first n terms. If a11 = 0, S14 = 98 (1), the general term formula of {an} can be obtained (2) Under the condition of (1), find the first n terms and TN of the sequence {an}

S14=(a1+a14)*7=98
a1+a14=14
a1+a1+13d=14
2a1+13d=14 (1)
a11=a1+10d=0 (2)
So d = - 2, A1 = 20
an=20-2(n-1)=-2n+22
(2) When an = - 2n + 22 > = 0, N11, an
Resistance R1 = 8 Ω, DC motor internal resistance R2 = 2 Ω, when switch S is off, R1 consumes 2.88w of electric power, the power efficiency is high
When k is off, R1 consumes 2.88w, R1 current I = 0.6A, voltage at both ends of R1 u = 4.8V, power internal resistance R0 = (6v-4.8v) / 0.6A = 2 Ω, when k is closed, R1 consumes 2W, R1 current = 0.5A, voltage at both ends of R1 u = 4V, power output current: (6v-4v) / 2 = 1a, motor current = 1a-0.5a = 0.5A; motor
Know the side length of the triangle, get the height, do not use the area formula
h²=b²-x²h²=a²-(c-x)²b²-x²=a²-(c-x)²x=(b²-a²+c²)/2ch²=b²-x²=b²-[(b²-a²+c²)/2c]²
Let the first term A1 and tolerance D of the arithmetic sequence {an} be integers, and the sum of the first n terms be SN. If a11 = 0 and S14 = 98, find the general term formula of the sequence {an} and the maximum of Sn
a11 = a1 + 10d = 0
S14 = 7(2a1 + 13d) = 98
The solution is as follows
a1 = 20
d = -2
So an = a1 + (n - 1) d = 20 - 2 (n - 1) = - 2n + 22
Because a11 = 0, d < 0
When n = 10 or n = 11, Sn maximum = 110
From the meaning of the title
a1+10d=0
The solution of A1 × 14 + 91d = 98 is A1 = 20 d = - 2
an=20+(n-1)×（-2）=22-2n
22-2n ≥ 0, n ≤ 10 is the sum of the top ten items and the maximum
S10 = 20 × 10 + 45 × (- 2) = 110, that is, the maximum value of 110
A11 = a1 + 10d = 0, S14 = 14a1 + 91d = 98, so d = - 2, A1 = 20
So an = - 2n + 22, the maximum SN is S10 or S11, which is 110
R2 has two separate power switches, R1 and R2 have two separate power switches, R1 and R2 work separately
At this time, the electric power of R1 is 90W, Q: what is the total power after closing
R1r2 should be parallel, because it is closed, so no matter whether the sub switch is open or closed, the voltage at both ends of the closed resistor must be the power supply voltage. According to the formula P = u ^ 2 / R, as long as one switch is closed, the closing of the other switch does not affect the power of the closed resistor, so the total power is p total = P1 + P2 = 1090
R1 and R2 are in parallel. After closing, the total power is 1090w.
What about the picture?
Why is the area formula of triangle base x height △ 2?
Because any triangle and its replica can be combined into a corresponding parallelogram. The area of the parallelogram is the base times the height, because it is composed of two identical triangles. Of course, the area of one of them is half of the parallelogram
A triangle is equivalent to a rectangle, which is cut half by the diagonal. If the area of the rectangle is multiplied by its width, the triangle is equal to its area divided by 2
Because the known conditions are bottom and high! There are many formulas for the area of triangles, and the bottom x height △ 2 is just one of them. When the known conditions are not base and height, the area formula is not base x height △ 2.
It is known that the sum of the first n terms of the arithmetic sequence an is Sn, and S13 > S6 > S14, A2 = 2,1
First of all, we use the formula Sn = Na1 + n (n-1) d to get S13 = 13a1 + 78d, S6 = 6A1 + 15d, S14 = 14a1 + 91da2 = a1 + D, and get A1 = 2-D. substituting the above formula, then S13 = 26 + 65D, S6 = 12 + 9D, and S14 = 28 + 77d. Then we use S13 > S6, that is, 26 + 65D > 12 + 9D, and get d > (- 1g4) S6 > S14, that is, 12 + 9D > 28 + 77d, and get D
Resistance R1 = 6ohm and R2 = 12ohm are connected in parallel in the circuit. The electric power consumed by R1 is 6W. How much voltage is the two ends of R1? (2) What is the total electrical power consumed by R1 and R2?
(1) ∵ R1 = 6 Ω, P1 = 6W, the voltage at both ends of R1 is: U1 = P1, R1 = 6 Ω × 6W = 6V. Answer: the voltage at both ends of R1 is 6V. (2) resistance R1 and R2 are in parallel, we can see that: u = U2 = U1 = 6V, ∵ R2 = 12 Ω, ∵ P2 = u22r2 = (6V) 212 Ω = 3W, then the total power consumed by R1 and R2 is: P = P1 + P2 = 6W + 3W = 9
If the area and base of a triangle are known, how to find its height formula?
Area * 2 / bottom = high
This formula is very common!
It will be used in the future!
Must remember!
In this case, find out whether there is the largest difference of the sequence {S12. D}
a(n)=a+(n-1)d.
S(n)=na+n(n-1)d/2.
24 = a(2) = a + d,a = 24-d
S(13)=13a+13*6d > S(6)=6a+3*5d > S(14) = 14a + 7*13d,
13a + 13*6d > 6a + 15d,0 < 7a + 53d = 7(24-d) + 53d = 7*24 + 46d,d > -84/23.
6a + 15d > 14a + 7*13d,0 > 8a + 76d,0 > 2a + 19d = 2(24-d) + 19d = 48 + 17d,d < - 48/17.
-84/23 < d < -48/17.
S(n) = na + n(n-1)d/2 = n(24-d) + n(n-1)d/2 = (d/2)n^2 + n[24-3d/2]
= (d/2)[n^2 + n(48/d - 3) + (48/d - 3)^2/4 - (48/d - 3)^2/4]
= (d/2){[n+(48/d-3)/2]^2 - (48/d-3)^2/4}
-84/23 < d < -48/17,
-23/84 > 1/d > - 17/48,
-92/7 > 48/d > -17,
-92/7 - 3 > 48/d - 3 > -20.
-8 > -113/14 > (48/d-3)/2 > -10.
n-8 > n+(48/d-3)/2 > n-10.
The largest term of S (8), s (9), s (10) is the largest term of S (n)