math-G.P and A.P

posted by .

A) which down the first G.P 5+10+20+.....to exceed 400000?
B) in an A.P,the sum of the first five term is 30, and the third term is equal to the sum of the first two. Write the first five terms of the progression.

  • math-G.P and A.P -

    A)
    a=5, d=5 , n = ? , Sum(n) ≥ 400 000
    (n/2)(10 + (n-1)(5)) ≥ 400 000
    n(5n + 5) ≥ 800 000
    5n^2 + 5n - 800 000 ≥ 0
    n^2 + n - 160 000 ≥ 0

    Now I took √160000 = 400
    so if the above had been
    n^2 + n - 159999 it would have factored to
    (n+401)(n-399)

    so our equation must have a solution between 399 and 401.
    Since n must be a whole number,
    sum(399) = (399/2)(10 + 398(5)) = 399000
    sum (400) = (400/2)(10 + 399(5)) = 399200
    sum(401) = (401/2)(10 + 400(5)) = 403005

    So you need 401 terms to exceed 400000

    B) "the sum of the first five terms is 30" ---> (5/2)(2a + 4d) = 30
    2a + 4d = 12
    a + 2d = 6
    "the third term is equal to the sum of the first two" ---> a+2d = a + a+d
    a = d

    sub that into first equation:
    d + 2d = 6
    d = 2 , then a = 2

    first 5 terms: 2 , 4 , 6, 8, and 10

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Precalculus

    The 8th term in an arithmetic sequence is 5, and the sum of the first 10 terms is 20. Find the common difference and the first term of the sequence. Alright so in an arithmetic squence the difference d between any two successive numbers …
  2. math

    In a Geometric progression the sum of its first 4 term is equal 15, and the sum of the next term is equal to 15/16. find its first term and its common ratio
  3. math

    The sum of the first 10 terms of an arithmetic series is 145 and the sum of its fourth and ninth term is five times the third the..determine the first term and constant difference
  4. math

    The third term of a G.P is 24 and the sum of the first two terms is 288. If all the terms are positive,find a)the first term and the common ratio b)the sum of all the terms from 4th term to the 8th term
  5. math

    The sum of the first 10 term of an arithmetic sequence is 145 and the sum of the fourth and ninth term is five times the third term. Determine the first term and constant difference.
  6. mathematics

    the 10th term of an arithmetic sequence is equal to the sum of 40 and 5th term.If the 15th term is 127 what is its common difference?
  7. maths

    In an arithmetical progression,the sum of the first five terms is 30,and the third term is equal to the sum of the first two.write down the first five terms of the progression.
  8. math

    The third,fourth and eight term of A.P form first three consecutive term of G.P.if the sum of the first ten term of A.P is 85.calculate the first term of both A.P and G.P,common ratio and sum of 5 term of G.P
  9. math

    The third,fourth and eight term of A.P form first three consecutive term of G.P.if the sum of the first ten term of A.P is 85.calculate the first term of both A.P and G.P,common ratio and sum of 5 term of G.P
  10. Math

    The first term of GP exceed the second term by 2 and the sum to infinity is 15 find the series and the sum of first 5 term

More Similar Questions