SOLUTION: A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Sn: 1 + 4 + 7 + . . . + (3n - 2) = n(3n - 1)/2 pls show step b

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Question 1075776: A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely.
Sn: 1 + 4 + 7 + . . . + (3n - 2) = n(3n - 1)/2
pls show step by step answer
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
1.  You are given an Arithmetic sequence with the first term 1 and the common difference of 3.

    They ask you about the sum of the first "n" terms of the sequence.



2.  On arithmetic progressions and the sums of their terms see the lessons

        - Arithmetic progressions

        - The proofs of the formulas for arithmetic progressions 

        - Problems on arithmetic progressions  

        - Word problems on arithmetic progressions

    in this site.


3.  On the method of Mathematical induction and its applications to calculating the sums of Arithmetic progressions see the lesson

        - Mathematical induction and arithmetic progressions

    in this site.

Concretely, the last lesson and its Problem 1 are very close to your problem.

So my advise to you is to read the referred lessons, and then you will be able to solve your problem on your own.

In this way you will learn everything what is important and related to arithmetic progressions, and, in addition,
you will learn the method of Mathematical induction.


You are at the right place and in good hands.



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