1.Write 4+6+8+10 in sigma notation:
I came up with sigma in the middle
3 on top
j=0 on the bottom
2n+4 to the right of the signma sign
2. Find the 10th term of the sequence
-1/5,-1/20,-1/80 this was a geometric sequence so I said a(subscript10) = -1/5*1/4^(10-1)
=-1/5*(1/4)^9 = -1/5*1/2621444
= -1/1310702
Should be sigma sign not signma sign
1. either have n=0 under the sigma, or use (2j+4) as the summand.
2. good work, but
4^9 = 262144. you have an extra 4.
1/5 * 1/262144 = 1/1310720
that dyslexia will get you every time. I noticed it right off, because no multiple of 5 ends in 2 :-)
did you hear about the dyslexic devil worshiper? He sold his soul to Santa.
Thank you-I see where I made the mistake
Funny!! I like that!
1. To write the expression 4 + 6 + 8 + 10 in sigma notation, you've correctly identified the summation symbol (sigma) in the middle. The expression 4 + 6 + 8 + 10 represents a finite series of terms, where each term is obtained by adding multiples of 2 to an initial term. In this case, the initial term is 4 and the common difference between consecutive terms is 2.
In sigma notation, you need to specify the index variable, the lower limit, the upper limit, and the expression for each term. Let's break it down:
- The index variable is usually denoted as "i" or "j." In this case, you've chosen "j," which is perfectly fine.
- The lower limit, "j = 0," indicates that the series begins when "j" is equal to 0.
- The upper limit, "3," signifies the final term of the series when "j" is equal to 3.
Now, let's focus on defining the expression for each term. You correctly stated that the terms are given by "2n + 4." However, it seems like you mistakenly used "n" instead of "j" in your explanation. To fix this, we can adjust the expression to "2j + 4."
Putting it all together, the sigma notation for 4 + 6 + 8 + 10 would be:
∑(2j + 4) (from j = 0 to 3)
2. You are given the geometric sequence: -1/5, -1/20, -1/80. To find the 10th term, you correctly noted that this is a geometric sequence with a common ratio. The general formula for finding the nth term of a geometric sequence is:
an = a * r^(n-1)
In this case, the first term (a) is -1/5, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:
r = (-1/20) / (-1/5) = 1/4
Now, we can substitute these values into the formula to find the 10th term:
a10 = (-1/5) * (1/4)^(10-1)
= (-1/5) * (1/4)^9
= (-1/5) * (1/262144)
= -1/1310720
Therefore, the 10th term of the given geometric sequence is -1/1310720.