How do I find the 11th term?

Question

So, the first terms are 16, 8, 4...

(The process of going smaller is continued indefinitely)

What is the 11th term?

What is the sum of all those terms?

Answer 1

the eleventh term is 0.015625

the sum is 31.734375

explanation given above is correct!!!!!

Answer 2

You can choose any answer you want but what they are looking for is probably is that the next number is half of the previous. so the eleventh is 0,015625. And the sum is 16+8+4+2+1+0.5+0,25+0,125+0,0625

+0,03125+0,015625=31,75

Answer 3

This is a geometric sequence. All of the terms are being multiplied by a common ratio which in this case is 0.5.

The 11th term uses this formula an = a1r^(n-1) where n is the number of terms, and a1 is the first term. So using this a11 = 16(0.5)^(10).  (Sorry don't have a calculator handy)

The sum follows another formula which is An=a1(1-r^n)/(1-r). So using this we get A11=16{1-(0.5)^11}/1-(0.5)=31.984375

This ONLY works for geometric sequences. There are also arithmetic sequences in which the sequences go up by a common difference.

Answer 4

this is a Geometric series with common ratio 1/2

r =1/2,a=16

nth term of a GP is

Tn=a*r^(n-1)

so 11th term =T11=16*(1/2)^10

T11=1/64

sum of 11 terms

Sn=a(1-r^n)/(1-r)

S11=16{1-(1/2)^11}/1-(1/2)

=31.984375

Answer 5

First term = 16

Second term = 8 = (1/2)(16)

Third term = 4 = (1/2)(1/2)(16) = (16)(1/2)^2

nth term = (16)(1/2)^(n - 1)

11th term = (16)(1/2)^(11 - 1)

= 16(1/2)^(10)

= 16(1/1024)

= 1 / 64

************

The formula for the sum is

S = a(1 - r^n) / (1 - r)

where a is the first term, r is the multiplier, and n is the number of terms.

So...

S = (16)(1 - (1/2)^11) / (1 - 1/2)

= (16)(1 - 1/1024) / (1/2)

= 32 (1023/1024)

= 31.96875