SOLUTION: Find S10 for the series 2 + 7 + 12 + 17 +...

Question 1126515: Find S10 for the series 2 + 7 + 12 + 17 +...
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Series appears to be like 2+12+22+32+... ADDED TO 7+17+27+37+...
OR
The series for ADDED TO the series for .

If you want the series for the first 10 terms, then
using the arithmetic sum formula

.
....

Do the sum of both of these for their FIRST FIVE TERMS.
Use sum of arithmetic series formula.
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

            Let me re-formulate the question / the problem in more clear way:

Find the sum S10 of the first 10 members of the sequence 2, 7, 12, 17, . . .

Solution

It is an arithmetic progression with the first term of 2 and the common difference of 5. The sum of the first 10 terms is = = (2+22.5)*10 = 24.5*10 = 245.

Answer. 245.

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

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.

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