posted by .

three number form an arithmetric sequence. Their sum is 24.
A)If 'a' is the first number and 'd' the common difference, show that a+d=8
B)If the first number is decreased by 1 and the second number by 2, the three numbers then form a geometric sequence. Find the three terms.

  • maths -

    your last 3 postings all deal with the basic definitions of sequences and series and involve translating the English statements into mathematical expressions.

    Why don't you show me what you have done for this one so far, and I will gladly help you further.

  • maths -

    ok cool... a) S/n=n/2 [2a+(n-1)d]
    B)i don't know from here hey...
    my name is marco

  • maths -

    ok Marko, it would have been easier to just do this
    a + a+d + a+2d = 24
    3a + 3d = 24
    a + d = 8

    b) so now we know that a = 8-d

    "If the first number is decreased by 1" so term1 = a-1
    " the second number by 2" , so term2 = a+d - 2

    our new terms are then
    t1 = a-1 = 8-d - 1 = 7-d
    t2 = a+d-2 = 8-d-d-2 = 6
    t3 = a+2d = 8-d + 2d = 8+d

    now these form a GS

    6/(7-d) = (8+d)/6

    take over.

  • correction - maths -

    near the end I had a typo but it did not cause an error

    t2 = a+d-2 = 8-d-d-2 = 6 should have been

    t2 = a+d-2 = 8-d+d-2 = 6

  • maths -

    ok thx.. i got 36=(8+d)(7-d)
    36= 56-8d+7d-d squared
    d=4 d=-5

  • maths -

    Nice, see how easy they are ?

  • maths -

    ya thx a ton

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra

    three times a first number decreased by a second number is 25. the first number increased by four times the second number is -22. find the numbers
  2. math

    Three numbers in an arithmetic sequence sum to six. If you add 1 to the first number, 2 to the second number, and 5 to the third number, the result will be a geometric sequence. What are the original 3 numbers?
  3. Grade 8 Math

    Can you write them in Mathematical/numbers form I'll solve them myself. i don't really get it though i have written the first one in mathematical for but i'm not sure if that's right. 1. When six is subtracted from five times a certain …
  4. Please help quick! Math

    The sum of three times a first number n twice second number is 8. If the second number is subtravted from twice the first number, the result is 3, find the numbers.
  5. Math

    The sum of three times a first number and twice a scond number is 43. If the second number is subtracted from twice the first number, the result is -4. Find the number. Mainly I can't figure out is this is two problems in one or just …

    The sum of five times a number and twice a second number is 18, but the difference of three times the first number and seven times the second number is -22. Find the two numbers using the elimination method.
  7. algebra

    Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number. The second number is equal to the sum of the first …
  8. Math

    The sum of three numbers equal 92. The second number is 8 more than the first number. The third number is 2 times the second number. What is the first number?
  9. show low high school

    he first number is 3 more than the second number. the sum of the number is 25. find the number.
  10. Maths

    Three numbers are in the ratio 2:3:5. The first number, second number reduced by 5 and the third number form an arithmetic sequence. Then the three numbers are

More Similar Questions