Enginpasa1 wrote:If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?
1,800
1,845
1,890
1,968
2,016
I am having troubles trying to understand these types of questions. I am wondering if anyone can show me where to go to learn ALL about this topic. I almost always get snagged by this and would liek to master it!
qa is D
the whole Sn Sn-1 thing is just there to scare you; in fact, these sequences (called
recursive sequences) are actually EASIER to understand than 'traditional' sequences defined by a formula. here's why:
'Sn' can be thought of as just 'the
current term', or 'the term i'm thinking about right now'
'Sn-1' can be thought of as 'the
previous term', or 'the term immediately before the one i'm thinking about right now'
so ...
you can read the given formula as, 'to get any term of the sequence, you add 6 to the previous term'. that's easy to think about.
alternatively, you can just look at the terms they give you and extract the pattern; even if you don't understand the formula right away, the odds are good that you'll be able to see the pattern by looking at the numbers.
--
these sequences don't usually have a separate chapter in anyone's math book because they're
arithmetic sequences; they follow
the same rules as sequences of consecutive integers, consecutive odds, or consecutive evens, which are really jsut special cases of arithmetic sequences. namely, they follow these rules:
* the average (arithmetic mean) of all the numbers in the sequence is the same as the median of the sequence
* the sum of all the terms in the sequence can be calculated as (number of terms) x (median), a fact that follows from the fact above
* the sum of all the terms can also be calculated as (1/2) x (number of terms) x (sum of first + last terms)
that's probably about all you have to know about these sequences. remember, all these facts work for sequences of consecutive odds, consecutive evens, and consecutive integers.
