Math sequences

Determine the smallest interger n such that 1+(4/5)+(4/5)^2+...+(4/5)^n>4.9
Please explain ti me about thisquestion. I can'tunderstand it.

  1. 👍
  2. 👎
  3. 👁
  1. you have a geometric series with
    a = 1 and r = 4/5

    sum(n) = a(1 - r^n)/(1-r) > 4.9

    1(1 - (4/5)^n)/1/5 > 4.9
    1 - (4/5)^n > .98
    (4/5)^n < .02

    suppose we let .8^n = .02
    log .8^n = log .02
    n = log.02/log.8 = 17.53

    testing:
    if n = 17 , sum(17) = (1 - .8^17)/.2 = 4.8874 < 4.9
    if n = 18 , sum(18) = (1-08^18)/.2 = 4.9099 > 4.9

    So the smallest value of n is 18

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chemistry

    Ranking equilibrium constants from largest to smallest according to an image?Ethene (C2H4) can be halogenated by the following reaction: C2H4 (g) + X2 (g) ->

  2. Chemistry

    Write the half reactions and the balanced equation for the galvanic cell Cu(s)| Cu2+(aq)|| Cu+(aq)| Cu(s). What is the smallest possible integer coefficient of Cu2+(aq) in the combined balanced equation? When put together the

  3. Math

    Alice earns 1.5 times her hourly rate for each hour she works after 40 hours in a week. She worked 50 hours this week and earned $660. What is her normal hourly rate? I know her average rate is $13.20, but I know that's not what I

  4. Math

    Which of these numbers is the smallest? 0.24, 0.02, 0.11, 2, 0 (Is 0 considered to be the smallest number here?)

  1. math

    what is an acrostic poem for interger?

  2. maths

    a triangle has sides of length 7 cm ,15cm and x cm. If x is an interger find (i) the minimum value of x (ii) the maximum value of x

  3. Plz help me..just one MATH question

    The number 1 is both the square of an integer and the cube of an integer. What is the next larger interger which is both a square and a cube of a positve integer. plz help, the only number i can think of was 0 but its smaller than

  4. physics

    pipe to know how the inner diameter changes. Rank in order from largest to smallest the gas speeds va, vb, and vc at points a, b, and c. Explain in complete sentences.

  1. Chem21

    Rank these gases in order of increasing standard molar entropy: Column preview Smallest S Br2(g) Second smallest S F2(g) Second largest S I2(g) Largest S Cl2(g) Matching pairs Smallest S Second smallest S Second largest S Largest

  2. physiology

    list from smallest to largest to smallest; atom, bacteria, sugar molecule, or ribosome

  3. Math

    Use algebra to determine the location of the vertical asymptotes and holes in the graph of the function. (Enter your answers from smallest to largest.) g(x)= 2x^2/x^4-x^2

  4. math

    Given the system of inequalities below, find the vertices of the feasible region. Report your vertices starting with the one which has the smallest x-value. If more than one vertex has the same, smallest x-value, start with the

You can view more similar questions or ask a new question.