SOLUTION: The sum of the first 5 terms of an AP is 30 and the fourth term is 44 find the common difference and the sum of the first 10 terms

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Question 1063744: The sum of the first 5 terms of an AP is 30 and the fourth term is 44 find the common difference and the sum of the first 10 terms
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
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The sum of the first 5 terms of an AP is 30 and the fourth term is 44 find the common difference and the sum of the first 10 terms
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Let "x" be the THIRD term and "d" be the common difference. 

Then the first 5 terms of the progression are

x - 2d, x-d, x, x+d, x + 2d,

and their sum is 5x.

Since the sum of the first 5 terms of the AP is 30, you have this equation

5x = 30,  which implies x = 6.

So, you just found the third term. It is 6.

Now, since the 4-th term is 44, the common difference is 44-6 = 38.

Then the second term is 6-38 = -32 and the first term is -32 - 38 = -70.

So, you know all and everything about the progression: The first term is -70 and the common difference is 38.

Can you complete the assignment on your own from this point ?

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".


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The sum of the first 5 terms of an AP is 30 and the fourth term is 44 find the common difference and the sum of the first 10 terms 
d, or common difference = 38



Formula for the sum of the 1st 10 terms of the series: 

Substitute 10 for n, - 70 for , and 38 for d to find the sum of the 1st 10 terms. 

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