|
Question 1190617:
Consider the arithmetic series 3+7+11+15+19, answer the questions below
a (i) T1 and S1
(ii) Express T2 in terms of S2 and S1
(iii) T4 and S4
(iv) Express T3 in terms of S4 and S3
Use the pattern you observed in previous questions to express T100 in terms of S100 and S99
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
(a)
(i) T1 is the first term, which is 3.
S1 is the first term, which is 3, again.
T2 is the second term, which is 7.
S2 is the sum of the first two terms, which is 3+7 = 10.
(ii) T2 = S2 - S1, which is OBVIOUS.
(iii) T4 is the 4th term 15.
S4 is the sum of the first 4 terms 3 + 7 + 11 + 15.
(calculate it on your own, if you need)
(iV) T3 = S3 - S2.
which means that the third term of the AP is the sum of the first 3 terms MINUS the sum of the first two terms.
If you think one minute, you will find this formula OBVIOUS and trivial.
And the last assignment /formula is
T100 = S100 - S99.
It expresses that obvious fact that the 100th term is the sum of the first 100 terms MUNIS the sum of the first 99 terms.
Happy learning (!)
------------------
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.
|
|
|
| |
