SOLUTION: What will be the sum of 3+7+11+15+19 ________ upto 80 terms

Algebra.Com
Question 1103960: What will be the sum of 3+7+11+15+19 ________ upto 80 terms
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


The first term is 3 and the common difference is 4; so the 80th term is 3+79*4 = 319.

Let's write the beginning and end of the series of numbers:
3+7+11+15+ ... +311+315+319

Because the terms in the sequence are equally spaced, the 80 terms in the sequence can be grouped into 40 pairs, each with the same sum:
(3+319), (7+315), (11+311), ....

So the sum of all 80 terms is the sum of 40 pairs, each with a sum of (3+319)=322. That means the sum of the 80 terms is 322*40 = 12880.
Answer by ikleyn(52914)   (Show Source): You can put this solution on YOUR website!
.
Arithmetic progression with the first term  = 3  and the common difference d = 4.


Use the general formula for the sum of the first n terms of an arithmetic progression


 =  = .


In your case it is   =  = 12880.

----------------
There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions


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.



RELATED QUESTIONS

Hello, how many terms of the sequence -19,-15,-11,... must be taken to give a sum of 98?... (answered by stanbon)
3 7 11 15 19 23 express T1 in terms of S1, express T2 in terms of S1 and... (answered by ikleyn)
what are the next 3 terms of this sequence -11, -2, 7,... (answered by JulietG)
sum of the numbers of the series: 6+9+21+69+261+........upto n terms (answered by Edwin McCravy)
The patterns array problem 1 2 3 4 5 6 7 8 9 (answered by richwmiller)
Please help me solve the following problems. I've tried to solve the problem but I don't (answered by venugopalramana)
Find the following upto 4 terms of expansion... (answered by Edwin McCravy)
Expand the following upto 4 terms of expansion (3-4x)power... (answered by Fombitz)
Can I please get some help? Cosider the following arithmetic sequences: (answered by robertb)