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(52879)   (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
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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(10556)  (Show Source):
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