# SOLUTION: The third term of an arithmetic sequence is 4 and the sum of the first 8 term is 36. Write down the first 8 term of the sequence.

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Question 217318: The third term of an arithmetic sequence is 4 and the sum of the first 8 term is 36. Write down the first 8 term of the sequence.

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The third term of an arithmetic sequence is 4 and the sum of the first 8 term is 36. Write down the first 8 term of the sequence.

Step 1. An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value

Step 2. Let x be the number to add or subtract in the sequence.

Step 3. Let a be the first term, let a+x be the second term, let a+2x be the third term, a+3x be the fourth term, and a+(n-1)x be the nth term

Step 4. Let a+7x be the 8th term. Then the sum of the first and eighth term is a+a+7x=2a+7x. The sum of the second term and seventh term is the a+x+a+6x=2a+6x. So four the first eight terms, there will be four pairs of 2a+6x which will equal to 36 or

Equation A

Also Equation B since the 3th term is 4.

Step 5. Then we have a system of equations given as Equations A and B. The following steps will solve the equation by substitution.

 Solved by pluggable solver: SOLVE linear system by SUBSTITUTION Solve: We'll use substitution. After moving 7*x to the right, we get: , or . Substitute that into another equation: and simplify: So, we know that x=0.333333333333333. Since , a=3.33333333333333. Answer: .

So a= and x=

So sequence is: , , , , , , , .

Check: The third term is and the sum is

Step 6. ANSWER: The sequence is , , , , , , , .

I hope the above steps and explanation were helpful.

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