# 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

- 1 decade agoFavorite 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.

- TheresaLv 44 years ago
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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 .....

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- James LLv 51 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.

You made a mistake 31+32 is 63 not 53

- 1 decade ago
2^n -1

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

- Anonymous1 decade ago
you have to write the seria until that number like this:the next number is the previous number*2+1

- Anonymous1 decade ago
next number would be 63 then 127

get it ?

- Anonymous1 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

Bookmark these for future ref.

31+32 = 63, not 53