What is the nth term of 1,2,4,8,16,32?

Answer 1

2^(n-1)

so you show 2^0, 2^1, 2^2, 2^3, 2^4, 2^5

Answer 2

This called a geometric sequence. Each term is formed by multiplying the previous term by a fixed number called r or the common ration In this particular sequence r = 2. The n'th term (Xn) is given by the formula:

Xn = ar^(n-1) (n = 1,2,3,...) where a is the firsdt term. So the formula for your sequence is:

Xn = 2r^(n-1)

Incidentally, giving the (n= 1,2,3,...) is important because here the 1st term is X1,

Sometimes it is more convenient to begin a sequence with
n= 0. Xo is then the first term and the formula would be:

Xn = ar^n (n= 0,1,2,...)

Note also that the way you have written the sequence means that is a finite sequence with 6 terms. Then the formula should be accompanied by (n =1,2,...6) If however your sequence goes on forever (an infinite sequence) then the sequence should be written as:

1,2,4,8,16,32,... The extra ... show it goes on forever.

Answer 3

well what you have there is an example of a 'geometric sequence'. that is a sequence of numbers that is generated by multiplying the previous term by a fixed constant called the 'common ratio'. the common ratio in this case is '2' as each term is twice that of its predecessor.

now the 'nth term' of a geometric sequence is given by:-

an = a r^(n-1)

the 'a' here is the first term and that is '1', the 'r' is the common ratio and that is '2', so we have our formula for the nth term as :-

an = 2^(n - 1)

as correctly predicted by everyone else

Answer 4

The nth term is 2^(n-1). The first term is 2^0
and each succeeding term is the next power of 2.

Answer 5

2 ^ (n - 1)

Answer 6

"""Term: 1"" 2"" 3"" 4"" 5 ------n
Number: 1"" 2"" 4"" 8" 16---2^(n - 1)

nth term is 2^(n-1)

Answer 7

2^(n-1)

Answer 8

216.