find the formula/ function?

Question

in the sequence: 1,3,7,15,31.
1 is term 1, 3 is term 2, 7 is term 3..so on and so forth. if the term is "n" what is the formula to find out the value of any term? can u explain how u got it in VERY simple terms?

also, can u give me a specific way to figure out more problems like this?

Answer 1

If you ignore the first term, then the pattern is
f(n) = 2^n - 1
For the second term, n = 2
f(2) = 2^2 - 1 = 4 - 1 = 3
Third term: n = 3
f(3) = 2^3 - 1 = 8 - 1 = 7
Fourth term: n = 4
f(4) = 2^4 - 1 = 16 - 1 = 15
I noticed that the numbers were close to powers of 2
2^1 = 1
2^2 = 4
2^3 = 8
2^4 = 16
With the exception of the first term, they all differed from a power of 2 by 1.

Answer 2

An = 2^n -1 for n = 1, 2, 3...

Answer 3

"sometimes" you look at the differences.
2-1 3-2 4-3 5-4
2, 4, 8, 16
The differences sort of pop out more than the numbers, heh?

this would indicate 2 raised to the term power.
Starting a 1, 2 to the 0
Going to 3 2 to the 2nd power

So -1 + 2 to the zero power = 1

(hard to write without exponents...)

-1 + 2 squared = 3
-1 + 2 cubed = 7
-1 + 2 to the fourth = 15
-1 + 2 to the fifth = 31

Answer 4

n = 2(n-1) +1

for example, computing term 3:
n = 2(3) + 1
n = 7

another example, computing term 5:
n = 2(15) + 1
n = 31

Answer 5

2n+1