Question 1

I do not understand how to find the n value. This did not make any sense to me. I need a formula or an explanation on how to find the n.

Accepted Answer

Another way you can do it is to come up with a function, and plug in your final value and solve for x. For example, when finding the sum of 3 + 5 + 7 + .... + 401 It might help to start out with a little chart:

x       f(x)
1       3
2      5
3      7
4       9

And from that you might intuit
f(x) = 2x + 1

Then plug in your final term, which is 401, and solve for x
401 = 2x + 1
400 = 2x
x = 200 tada

Sometimes you’ll see a slightly different, but equivalent function. For example, the same 3 + 5 + 7 + .... + 401 you might first identify as
f(x) = 3 + 2(x-1)
and that’s fine, because mathematically it’s the same function. Even if you don’t simplify it to 2x + 1 you still find x = 200 when you plug in your final term in the sequence.
401 = 3 + 2(x-1)
401-3 = 2(x-1)
398 = 2 (x-1)
398/2 = x-1
199 = x - 1
x = 200

Question 2

How do you determine the value of n? I don't think this was every explained.

Accepted Answer

n is the number of terms. Take the difference of the first and last term over the common difference and add 1 to get n.

Question 3

For problem 2: how did you find out the n was 450? I tried doing An-A1/2 and adding one for the first term and I got a different number.

Accepted Answer

it's like this...
let's say we have an arithmetic sequence that goes like 2, 4, 6, 8, ..., 262
lets take first term as a=2
common difference as d=2
last term or nth term as a(n)=262
we know the formula for nth term is a(n)=a+(n-1)d
so here, 262=2+(n-1)2
so n-1 = (262-2)/2 = 260/2 = 130
so n= 130+1 =131
Sal explained it in a non-formula, less mathematical more logic-based kind of way, but this is the mathematical basis for it
hope it helps :)

Question 4

How do we calculate the value of n

Accepted Answer

Take the LAST  number in the sequence MINUS the FIRST number in the sequence.
DIVIDE that value by the pattern in the sequence.
How do you find the pattern? Ask, "How do I get from the first term, to the second term?"
Hope that helps

Question 5

What's exactly the difference between "progression", "sequence" and "series"?

Accepted Answer

Progession and sequence are the same thing; a list of numbers generated according to some rule or rules.
For example 2,4,6,8,10 is an (arithmetic) sequence.
Or 1, 2, 4, 8, 16, which is a geometric sequence.

A series however is the SUM of a sequence or progression
eg  1 + ½ + ¼ + ⅛

There are a number of KA videos on this subject, here's one: https://www.khanacademy.org/math/algebra2/sequences-and-series/copy-of-geometric-sequence-series/v/series-as-sum-of-sequence

Question 6

Why is this so confusing?

HELP

Accepted Answer

Okay, for each series of terms given above, you fish out the 'first term(a), the common difference(d)->which is gotten by subtracting the previous term from the next {like now, 1+2+3+4...+10> in this, to get the common difference, you would subtract 1 from 2 or subtract 2 from 3. I'm sure you get the point, the subtraction should be progressive. This tells us that our common difference in this case is .....*drumrolls*....1, yes you got it!} and the number of terms (n) which is gotten by looking at the last term given and substituting it in this formula of "nth" terms, Tn= a+(n-1)d={the last term you see there}. By doing so, you would find your "n" successfully. With that formula, note that 'a', 'd' and 'n' are involved! When you are done doing all of this, you will then use the final formula for the Sum of the terms> Sn=n/2{2a+(n-1)d} to find the sum of the whole terms given in the series provided. I am confident that you get it now! If there is any other problem, please do not hesitate to reply or reach out!

Question 7

on problem 1, could someone tell me how they found out the number of terms was 450?

Accepted Answer

11+20+29+...+4052

They found n (the last term) by set 4052 into the explicit formula. So to find n you must know how to formulate the formula from the sequence.

This has the initial of 11 and common difference of 9, so a(n)=11+9(n-1). So to find what n is when a(n) = 4052, you set 4052=11+9(n-1) and solve for n. They didn't explain but that's how you would find n in that problem.

Question 8

What the heck does this mean: Find the sum of first 335 terms

A(sub)1 = 2
A(sub)i = A(sub< i -1 >) -3

What does the "i" mean?

Accepted Answer

The subscripted numbers denote the number of the term in series A. The subscripted i  can be any number other than 1. (The first term is separately defined.) The subscripted i-1 refers to the term immediately before term i.

Based on the example you gave, here are the first few terms. (The underscore is used to show a subscript.)
A_1 = 2
A_2 = A_1 - 3 = 2 - 3 = -1
A_3 = A_2 - 3 = -1 - 3 = -4
A_4 = A_3 - 3 = -4 - 3 = -7

Precalculus

Course: Precalculus > Unit 9

Arithmetic series

Find the sum of $1 + 3 + 5 + 7 + 9$ ‍.

Consider the series $3 + 5 + 7 + … + 401$ ‍.

Try it yourself

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