Maths

posted by .

1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is 4/3 less than the sum of the first 3 terms of the geometric progression.Determine the value of r,the common ratio of the geometric progression


2..a new sequence is formed by adding together the corresponding terms of a geometric sequence and an arithmetic sequence.The common ratio of the geometric sequence is 2 and the common difference of the arithmetic sequence is 2.The first term of the new sequence is 1,and the second term is 7...
2.1 calculate the third term of the new sequence
2.2write down an expression for the n-th term of the new sequence

  • Maths -

    a+d = ar
    a = 12
    r < 1
    3/2 (2a+2d) = a(1+r+r^2) - 4/3

    3ar = a(1+r+r^2) - 4/3
    36r = 12(1+r+r^2) - 4/3
    r = 2/3 or 4/3

    r=2/3:
    12+d = 12* 2/3
    d = -4

    AP = 12 8 4 0 ...
    GP = 12 8 16/3 32/9 ...

    check
    12+8+4 = 12+8+16/3 - 4/3 YES

  • Maths -

    4/3

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. arithmetic

    Each term of a progression is determined by adding 0.5 to the preceding term. the sum of the first 25 terms of the progression equals the square of the 25th term. calculate the possible value(s) of the first term
  2. maths

    1) The first term of arithmetic progression is -20 and the sum of it's term is 250. find it's last term if the number of it's terms is 10 2) Find the fifth term from the arithmetic progression -12, -9, -6 hence find the sum of it's …
  3. math

    The first, the third and the seventh terms of an increasing arithmetic progression are three consecutive terms of a geometric progression. In the first term of the arithmetic progression is 10 find the common difference of the arithmetic …
  4. MATHEMATIC DEPARTMENT

    The second, third and ninth terms of an arithmetic progression forms the first, second and third terms of a geometric progression. Find the common ratio and hence the eleventh term of geometric progression.
  5. algebra

    if 1, 2, 7 and 20, respectively, are added to the first terms of an arithmetic progression, a geometric progression of four terms is obtained. find the first term and common difference of the arithmetic progression the answers are …
  6. math

    The 3rd term of an Arithmetic Progression is 10 more than the first term while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the Arithmetic Progression if the 7th term is seven times the …
  7. math

    An arithmetic progression as the same first and second terms as the geometric progression. Find the sum of the first 20 terms of the arithmetic progression. How do I do this?
  8. math C2 sequences and series

    The eight,fourth and second terms of an arithmetic progression form the first three terms of a geometric series. The arithmetic progression has first term A and common difference d, and the geometric progression has first term G and …
  9. Algebra

    Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|<1 if the second term is (4/3) and the ratio of the sum of the squares of the terms of the progression to the sum of the terms of the …
  10. Math

    The third term of a geometric progression of positive terms is 18 and the fifth term is 162 Find the common ration and the first term?

More Similar Questions