I have this question and I don't understand what it's asking for. It says evaluate, is it asking for the missing term or what?
The sequence 21, 23, 25, 27, 29, ..., 41 has 11 terms. Evaluate the related series.
* 320
* 341
* 300
* 166
Very confused, any insight on how to solve this would be helpful :)
In simple terms, for a sequence you would list the terms,
in a series you would add the terms
so you want
21+23+25+ ... + 41
this is an arithmetic series with
a = 21, d=2 and n = 11
the sum of those terms
using sum = n/2(first term + last term)
= 11/2(21+41)
= 341
The way the question is phrased suggests that not all of it has actually been posted. "Evaluate the related series" doesn't mean anything on its own - at least, not to me. Has your teacher defined a "related series" to be the sum of the individual elements of that series? This is one of those questions where its easy enough to guess what's required - which is what has been written above - but this seems not actually to have been ASKED for!
To solve this question, you need to understand the terms "sequence" and "series."
A sequence is a list of numbers with a specific pattern or rule. In this case, the given sequence is 21, 23, 25, 27, 29, ... The pattern here is that each term is obtained by adding 2 to the previous term.
A series, on the other hand, is the sum of terms in a sequence. To evaluate a series, you need to find the sum of all the terms.
In this question, you are given the sequence 21, 23, 25, 27, 29, ..., 41, which has 11 terms. To find the sum of this series, you can use the formula for the sum of an arithmetic series:
Sn = (n/2) * (2a + (n-1)d)
Where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference between the terms.
Now let's plug in the values.
n = 11 (as there are 11 terms)
a = 21 (the first term)
d = 2 (since the common difference is 2, as seen in the pattern)
Sn = (11/2) * (2*21 + (11-1)*2)
= (11/2) * (42 + 10*2)
= (11/2) * (42 + 20)
= (11/2) * 62
= 341
Therefore, the sum of the series is 341.
So, the correct answer to the question "Evaluate the related series" is option "341".