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.

Algebra ->  Sequences-and-series -> 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.       Log On


   

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.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
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

4%2A%282a%2B7x%29=36

2a%2B7x=9 Equation A

Also a%2B2x=4 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:
+system%28+%0D%0A++++2%5Ca+%2B+7%5Cx+=+9%2C%0D%0A++++1%5Ca+%2B+2%5Cx+=+4+%29%0D%0A++We'll use substitution. After moving 7*x to the right, we get:
2%2Aa+=+9+-+7%2Ax, or a+=+9%2F2+-+7%2Ax%2F2. Substitute that
into another equation:
1%2A%289%2F2+-+7%2Ax%2F2%29+%2B+2%5Cx+=+4 and simplify: So, we know that x=0.333333333333333. Since a+=+9%2F2+-+7%2Ax%2F2, a=3.33333333333333.

Answer: system%28+a=3.33333333333333%2C+x=0.333333333333333+%29.



So a=10%2F3 and x=1%2F3

So sequence is: 10%2F3, 11%2F3, 4, 13%2F3, 14%2F3, 5, 16%2F3, 17%2F3.

Check: The third term is 4 and the sum is %2810%2B11%2B12%2B13%2B14%2B15%2B16%2B17%29%2F3=36

Step 6. ANSWER: The sequence is 10%2F3, 11%2F3, 4, 13%2F3, 14%2F3, 5, 16%2F3, 17%2F3.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra,
please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and
for Trigonometry please visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at
john@e-liteworks.com for your future math needs.

Respectfully,
Dr J