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There is an arithmetic sequence with tolerance of 4 and item number of 7. The total number is 147
Middle number: 147 △ 7 = 21
Other numbers are: 21-4 = 17,17-4 = 13,13-4 = 9,21 + 4 = 25,25 + 4 = 29,29 + 4 = 33
How to find tolerance in summation of arithmetic sequence?
Sum = (first item + last item) * number of items / 2
(on the premise of knowing the sum, the first item, the last item and the number of items)
(first item - last item) divided by (number of items - 1)
The sum of arithmetic sequence must be all Chinese sum = first term = last term = tolerance=
Sum is the sum of the first and last terms multiplied by the number of terms divided by two,
The first term is equal to and multiplied by two divided by the number of terms, and then the last term is subtracted,
The last term is equal to and multiplied by two divided by the number of terms, and then the first term is subtracted,
The tolerance is equal to the difference between any two adjacent terms and the difference between the last term and the first term divided by the number of terms
Why do we use the formula of arithmetic sequence? We need to use (last first) / tolerance plus 1
This is a formula for calculating the number of items in a sequence. According to the tree planting principle, there are n + 1 trees with n intervals, so we need to use (last first) / tolerance plus 1
What is the formula for finding the first term and the last term of an arithmetic sequence
For example, sequence 1, 3, 5, 7, 9
Obviously, it is an arithmetic sequence. Then it is found that the value of each adjacent two terms minus one is constant. This value is the tolerance
Then the first term is the first term of the sequence, which is 1
Item 1, 1
Item 2, 3
Item 3, 5
.
What is the nth term? Through the rule, we find that the relationship between the number of terms (that is, the nth term) and the corresponding value is twice and then minus 1
For example, 1 = 2 × 1-1
3=2×2-1
5=2×3-1
...
Then the nth term an = 2n - 1 is the last term
CN = (2n-1) * (1 / 2) ^ n is solved by dislocation subtraction
Cn+1=(2n+1)*(1/2)^n*(1/2)=(n+1/2)*(1/2)^n
An+1=Cn+1-Cn=(3/2-n)*(1/2)^n=(5-2(n+1))*(1/2)^(n+1)
an=(5-2n)*(1/2)^n
The application of the sum of the equal ratio sequence in Mathematics
A ball falls from a height of 30 meters. After landing, it jumps back to half of the original height and falls again. When it lands for the 10th time, the distance it passes is about () meters?
(please write the calculation process and step description)
The correct answer is 89.88 meters.
30+2[30×1/2+30×(1/2)^2+30×(1/2)^3+.+30×(1/2)^8]+30×(1/2)^9=89.88
The first landing and the last landing are one-way, and the middle several are return
The first time: 30 meters
The second time: 30 × (1 / 2) ^ 1
The third time: 30 × (1 / 2) ^ 2
And so on
The 9th time: 30 × (1 / 2) ^ 8
The 10th time: 30 × (1 / 2) ^ 9
So there is the above formula
Application of summation of equal ratio sequence (please attach specific ideas)
The output value of enterprise a in January is a, and the growth rate of monthly output value in the future is p. the total output value of enterprise a in one year is ()
According to the question, we can know that the output value in February is a (1 + P), and that in March is a (1 + P) ^ 2,
By analogy, the output value of each month is an = a (1 + P) ^ (n-1), and N represents the number of months
Obviously, the arithmetic sequence with A1 = a as the first term and q = 1 + P as the common ratio
Therefore, the total output value of enterprise a in one year is the first 12 items and S12
I can ask for it myself. I can't beat it out
On the summation of equal ratio sequence
How to sum from A1 to a (n-1)
How to sum from A3 to an
Total n-1 items
So A1 * [1-Q ^ (n-1)] / (1-Q)
Total n-3 + 1 = n-2 terms
So A3 * [1-Q ^ (n-2)] / (1-Q)
This year, my grandfather's age is six times that of Xiao Ming. In a few years, my grandfather's age will be five times that of Xiao Ming. In a few years, my grandfather's age will be four times that of Xiao Ming
Suppose grandfather is x years old, then Xiao Ming is y years old. The first year passed a, and the second year passed B, x = 6yx + a = 5 (y + a) x = 5Y + 4ax + A + B = 4 (y + A + b) x = 4Y + 3A + 3b solution x = 24a, y = 4A, B = 5A3 according to the actual a = 3, B = 5Y = 12x = 72 A: grandfather is 72 years old
RELATED INFORMATIONS
- 1. What is dislocation subtraction
- 2. Let the sum of the first n terms of the sequence an be Sn, and Sn = n ^ 2-4n + 4, BN = an / 2 ^ n. can we use dislocation subtraction to find the sum of the first n terms of BN and TN?
- 3. Let the sum of the first n terms of the equal ratio sequence {an} be Sn, S4 = 1, S8 = 17, and find the general term formula an
- 4. If the sum of the first n terms of the equal ratio sequence {an} is 2N-1, then the sum of the first n terms of the sequence {an ^ 2} is?
- 5. F (x) = sin (ω x + φ) (ω is greater than 0, φ is greater than or equal to 0 and less than or equal to π) is even function, and the distance between two adjacent highest points on the image is 2 π It is known that the function f (x) = sin (ω x + φ) (ω greater than 0,0 ≤ φ ≤ π) is even function, and the distance between two adjacent highest points on the image is 2 π 1. Find the analytic expression of F (x) 2. If a belongs to (- π / 3, π / 2), f (a + (π / 3)) = 1 / 3, find the value of sin (2a + (5 π / 3))
- 6. Are there overlaps between infinite discontinuities and oscillatory discontinuities, such as piecewise function x < 0, f (x) = 1 / x, x > 0, f (x) = sin Is there any overlap between infinite discontinuity and oscillation discontinuity For example, when the piecewise function x < 0, f (x) = 1 / x, x > 0, f (x) = sin (1 / x), what is the breakpoint of x = 0?
- 7. F (x) = the maximum of SiNx cosx
- 8. Given that - 90 degree is less than X and less than 0 degree, SiNx + cosx = 0.2, find SiNx cosx =?
- 9. It is known that the focus of the ellipse x ^ 2 / 4 + y ^ 2 = 1 is F1, F2, and the intersection of the parabola y ^ 2 = PX (P > 0) and the ellipse in the first quadrant is Q, if ∠ f1qf2 = 60 °, (1) Calculate the area of △ f1qf2; (2) Find the equation of this parabola
- 10. Point P is a point on the hyperbola x2 / 25-y2 / 9 with F1 and F2 as the focus, and the absolute value of Pf1 = 12, then the absolute value of PF2=
- 11. If the arithmetic sequence {an} satisfies A1 = 1, and A1, A2 and A4 are equal proportion sequence, find an
- 12. Observe the equation 1x2 = 1 / 2 minus 1 / 2, 2x3 = 1 / 2 minus 1 / 3, 3x4 = 1 / 3 minus 1 / 4 (1) Fill in the blanks according to the above rules (2) According to the above rules, the calculation is: 1x2 / 1 + 2x3 / 1 + 3x4 / 1 +... + 2012x2013 / 1 (3) If the value of a is the smallest positive integer and B is 3, find one part of AB + (a + 2) (B + 2) + (a + 4) (B + 4) +... + (a + 200) (B + 200)
- 13. Please write down the process and way of thinking Given an = 1 / N √ (n + 1) + (n + 1)) √ n, find the sum of the first n terms of the sequence If the deformation method of an can not be written in detail, the method can be written directly, but the important steps should be given It's an = (1 / N √ (n + 1)) + (n + 1) √ n. part of the plus sign in front of it is a fraction, but not after it~
- 14. A problem of summation of sequence It is known that an = (2n + 1) 2n Find SN
- 15. Sum, 1 / 4-1 / 8 + 1 / 16-1 / 32 +. - 1 / 1024 emergency
- 16. Sum: 1 + 3 + 5 + ＋(2n－1)
- 17. The derivation process and reason of the formula of acceleration measured by physical clock in grade one of senior high school Why must a = [(S6 + S5 + S4) - (S3 + S2 + S1)] / 9t ^ 2 not be a group of three? What is the grouping standard? Is it n / 2? What if n is odd?
- 18. Suppose that an object starts to move in a straight line when its initial velocity is 1, and the acceleration at any time t is known to be (2 root sign T) + 1. Try to express the displacement s as a function of time t
- 19. Uniform velocity linear motion is defined as the linear motion with constant acceleration. The acceleration of uniform velocity linear motion is 0, and the acceleration is also constant, Is uniform linear motion equal to uniform variable speed linear motion?
- 20. ① The magnitude and direction of the acceleration of the uniform speed change linear motion are invariable ① It must be right ② Is it right or wrong? If it is wrong, isn't it contradictory with (1)?