Find the twelfth term of the geometric sequence: 1/16, 1/8, 1/4....
Common ratio: 1/2
I got the ratio by dividing 1/16 by 1/8 which gave me 1/2 and I divided 1/8 by 1/4 to get 1/2-----That is how I got a common ratio of 1/2.
In order to obtain the 12th term I think I messed up somewhere:
a12=(1/16)(1/2)^12-1 which gave me 3.05E
I don't think that is right but don't know where I went wrong.
Help!!!
Thanks
3.05 E-5 not 3.05 E
Multiply by 1/2 11 times and the result is likely to be very small.
Well, it seems like you made a small mistake in your calculation for finding the 12th term of the geometric sequence. Let's see if we can fix that.
The formula to find the nth term of a geometric sequence is given by: an = a1 * r^(n-1)
In this case, the first term (a1) is 1/16 and the common ratio (r) is 1/2. We want to find the 12th term (a12).
Plugging in these values into the formula, we have: a12 = (1/16) * (1/2)^(12-1)
Simplifying further, we have: a12 = (1/16) * (1/2)^11
Now let's calculate this:
a12 = (1/16) * (1/2)^11
a12 = (1/16) * (1/2048)
a12 = 1/32768
So, the twelfth term of the geometric sequence is 1/32768.
I hope that clears things up for you. Remember, even clowns make mistakes sometimes!
To find the twelfth term of the geometric sequence, you need to use the formula:
an = a1 * r^(n-1)
where:
an is the nth term,
a1 is the first term, and
r is the common ratio.
In this case, the first term (a1) is 1/16, and the common ratio (r) is 1/2.
Plugging in these values into the formula, we can solve for a12:
a12 = (1/16) * (1/2)^(12-1)
= (1/16) * (1/2)^11
= (1/16) * (1/2)^11
= (1/16) * (1/2^11)
= (1/16) * (1/2048)
= 1/32768
So, the twelfth term of the geometric sequence is 1/32768.
To find the twelfth term of the geometric sequence, you need to use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where:
an is the nth term
a1 is the first term
r is the common ratio
n is the position of the term
In this case, the first term (a1) is 1/16, and the common ratio (r) is 1/2.
To find the twelfth term (a12), you would substitute these values into the formula:
a12 = (1/16) * (1/2)^(12-1)
= (1/16) * (1/2)^11
= (1/16) * (1/2048)
= 1/32768
Therefore, the twelfth term of the geometric sequence is 1/32768.
It seems that you made a mistake with the exponent in your calculation. Make sure that you raise the common ratio to the power of n-1, not n.