SOLUTION: In this arithmetic sequence wee are given that S1=9 AND S2=20 What is the 4th terms. Thanks for your help.

Question 1169395: In this arithmetic sequence wee are given that S1=9 AND S2=20
What is the 4th terms.
Thanks for your help.
Found 5 solutions by MathLover1, math_helper, ikleyn, MathTherapy, greenestamps:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

arithmetic sequence formula:
where n-th term, 1-th term, is the difference between two consecutive terms

you are given that:

so, given two consecutive terms and
and your formula is:

What is the 4th term? =>the 4th term means

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
So with an AP, you have common differences from one term to the next:

and means the common difference is 20-9 = 11.

Therefore where n = 1,2,3,...
Plug in n=4 to find
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
In this arithmetic sequence wee are given that S1=9 AND S2=20
What is the 4th term.
Thanks for your help.
~~~~~~~~~~~

            Pay your attention on how I edited your post to make it consistent with the English language.

            Also, your post does not define what the S1 and S2 are.

            Traditionally, and by default, Sn means the sum of n terms of an arithmetic progression,
            and I interpret it EXACTLY in this way.

            Two other tutors interpret it DIFFERENTLY.

            So, been so inaccurate in formulation your problem, you should not be surprising when you obtain different answers.

            It is TOTALLY and ENTIRELY YOUR FAULT.

The first term is = 9 (from S1 = 9). Hence, the second term is 20-9 = 11 (from S2 = 20). Thus the common difference is 11-9 = 2. Then the third term is 11+2 = 13, and the fourth term is 13+2 = 15. ANSWER

Solved, explained and completed.

-------------

For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
In this arithmetic sequence wee are given that S1=9 AND S2=20
What is the 4th terms.
Thanks for your help.

2 of them are WRONG!!

If the sum of ONE (1) number in the sequence is 9, then that means that the 1st term , or

If the sum of TWO (2) numbers in the sequence is 20, then that means that the 2nd term, or
Therefore, the common difference (d) is: 2 (11 - 9)
With each term, or a_n = a₁ + (n - 1)d, then the 4th term, or , or Just SIMPLY add 2(2), or 4 to the 2nd term, 11.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The statement of the problem is deficient.

While it is very often the case that the use of "Sn" when talking about an arithmetic sequence indicates the SUM of the first n terms, it is not a universally accepted convention.

The statement of the problem should either use the words "sum of n terms", or it should specify that the notation Sn represents the sum of n terms and not the nth term.

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