In the series 1 3 7 15 31: 3 occured the first time, 7 the second, 15 the third. Is there a formula for this?

When I am given a number from this series, how do I know whether it is the first, third, fifth, etc.?

11 Answers

Relevance
  • 1 decade ago
    Favorite Answer

    Hi,

    This is the pattern.

    1 3 7 15 31

    =>(2-1) (4-1) (8-1) (16-1) (32-1)

    => {(2^1)-1} {(2^2)-1} {(2^3)-1} {(2^4)-1} {(2^5)-1}

    See, its (2^n) -1

    Peace out.

  • 3 years ago

    1 3 7 15 31

  • 4 years ago

    For the best answers, search on this site https://shorturl.im/7v1bP

    I can't believe that no-one seems to have nailed this after 27 answers! Your question is "What *is* the pattern...". Your question is not "What is the next term" or something similar. In other words, it's not just about saying "start with a number, double it and add 1, etc etc". That's fine if you know one term and want to figure out the next. What we really want to know is: "What is the value of the nth term of the sequence?" We want to be able to know what *any* term in the sequence is, whether we know the preceding one or not. You will see that the pattern is very close to the pattern 2, 4, 8, 16, 32... etc. Each term in our sequence has a value of 1 less. You will also see that the 2, 4, 8, 16, 32 sequence consists of powers of 2. So the first term is 2^1 = 2, the second is 2^2 = 4, the third is 2^3 = 8 and so on. The nth term in that sequence is 2^n. But that's not exactly what our sequence is. As we said above, our sequence is similar, with each term being 1 less than the "powers of 2" sequence. The nth term in our sequence is therefore (2^n) - 1 Or, if you prefer, f(n) = (2^n)-1

  • 1 decade ago

    1+2 = 3

    3+ 4 = 7

    7+ 8 = 15

    15 + 16 = 31

    if u look at the addition and right number..every time u r adding double of the previous number u added..2,4,8,16 the next number would 31+32 = 53 and the next number would be 53+64= 117..etc..

    1 3 7 15 31 53 117 245 .....

  • How do you think about the answers? You can sign in to vote the answer.
  • 1 decade ago

    The formula for the nth term in the sequence is 2^n - 1.

    2^1 - 1 = 2-1 = 1

    2^2 - 1 = 4-1 = 3

    2^3 - 1 = 8-1 = 7

    and so on.

  • 1 decade ago

    2^n -1

    when given a number add 1 to it and take the logarithm base 2 of what u get

  • Anonymous
    1 decade ago

    you have to write the seria until that number like this:the next number is the previous number*2+1

  • Anonymous
    1 decade ago

    next number would be 63 then 127

    get it ?

  • Anonymous
    1 decade ago

    http://mathforum.org/library/drmath/view/56985.htm...

    This is either exact or quite close.

    It's called the "kth term" or "nth term."

    http://www.mathworld.wolfram.com

    http://www.khake.com/page47

    Bookmark these for future ref.

  • raj
    Lv 7
    1 decade ago

    the next numberis 2n+1

    1,2(1)+1,2(3)+1,2(7)+1,.

    2(15)+1,2(31)+1..................

Still have questions? Get your answers by asking now.