ARATMETICS

posted by .

THE ARITHMETIC PROGRESSION 2,5,8,11 AND 3,10,17,24... HAVE SOME COMMAN VALUES.WHAT IS THE LARGEST VALUE LESS THEN 500 THAT THEY HAVE IN COMMAN?

  • ARATMETICS -

    the nth term in the first:
    an= 2+3n
    the mth term in the second:
    yn= 3+7m

    if an=ym
    an-ym=0
    3n-7m=1
    3n=7m+1

    this means above that 7m +1 is divisible by 3 3,6,9,12,15 (see that m=2 works, and n=5).
    Lets look at the divisibility rule at the high end.

    7m+1 divisible by three; 501, 498, 495, 492, .... Now, which of those minus one are divisible by 7?
    489, 486, 483, ...
    Another method is multiplication by 3. A number of the form 10x + y has the same remainder when divided by 7 as 3x + y. So get the leftmost digit of the original number, multiply by 3, add the next digit, get the remainder by 7, and continue from the beginning: multiply by 3, add the next digit, etc. For example, the number 371: 3×3 + 7 = 16 remainder 2, and 2×3 + 1 = 7. This method can be used to find the remainder of division by 7

    So here subtract one, then test.
    489, 486, 483, ...
    3*4+8=20 r 6, 3*6+8=24 not divisible
    485: 3*4+8=2r6, 3*6+5=23 not divisible
    482: 3*4+*=2r6, 6*3+2=20 not divisible
    479: in my head, 2r5, 15+9=24 not div
    476: 2r5, 15+6=21 divisible...

    so 7y+1=477, or 7y=476
    3n-7y=1 or 3n=477
    solve for n, m and you have it.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Comman Sense

    What does cupid shooy from his bow to make people fall in love?
  2. Comman Sense

    What are symbols of love. (Im doing a crossword puzzle) _E_ _ _ S Can you fill the blanks?
  3. wo9rld history

    what dose a 16 making pictures of a bomb and threating a school have in comman with world history what is the text to text to that
  4. arithmetic

    Two arithmetic progression have thd same first and last terms.the first arithmetic progression has 21 terms with a common difference of 9.How many terms has the other arithmetic progression if its common difference is 4?
  5. AP Calculus

    The 9th term of an arithmetic progression is 4+5p and the sum of the four terms of the progression is 7p-10, where p is a constant. Given that common difference of the progression is 5, find the value of p.
  6. Math

    A sequence is called an arithmetic progression of the rst order if the di erences of the successive terms are constant. It is called an arith- metic progression of the second order if the di erences of the successive terms form an …
  7. Maths

    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 …
  8. Math

    5 distinct positive reals form an arithmetic progression. The 1st, 2nd and 5th term form a geometric progression. If the product of these 5 numbers is 124 4/9, what is the product of the 3 terms of the geometric progression?
  9. Math (Geometric Progression)

    5 distinct positive reals form an arithmetic progression. The 1st, 2nd and 5th term form a geometric progression. If the product of these 5 numbers is 124 4/9, what is the product of the 3 terms of the geometric progression?
  10. 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 …

More Similar Questions