SOLUTION: Find the indicated partial sum for the given sequence. Show the solution 4,7,10,13,...,S10

Question 1184340: Find the indicated partial sum for the given sequence. Show the solution
4,7,10,13,...,S10
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
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Find the indicated partial sum for the given sequence. Show the solution
4,7,10,13,...,S10
~~~~~~~~~~~~~~~~~~~~~~~~

As the last term of the sequence, I see " S10 " in your post.

What do you mean using this non-numerical term " S10 " ?

Does it mean " the 10-th term " or the sum of the first 10 terms, or something else ?

For arithmetic sequences, there are well known formulas, written everywhere, in any textbook or in numerous Internet sites.

For example, you may look into the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site and to learn the subject from there . . .

Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Technically, the statement of the problem needs to specify that this is an arithmetic sequence. Simply showing the sequence as
4,7,10,13,...
leaves open the possibility that the following numbers could be ANY numbers.

Assuming then that this is an arithmetic sequence....

S10 is the sum of the first 10 terms of the sequence.

The sum of ANY set of numbers is the average of the numbers, multiplied by how many there are.

We are given the number of terms in this sequence; and, because the sequence is arithmetic, the average of all the terms is the average of the first and last.

In an arithmetic sequence, the n-th term is the first term, plus (n-1) times the common difference.

Armed with those ideas....

The common difference is 3; the first term is 4; so the 10th term is 4+9(3)=31.
The average of the terms is the average of the first and last: (4+31)/2=35/2.
The sum of the first 10 terms is 10(35/2)=5*35=175.

ANSWER: S10 = 175

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