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. 


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+7x)=36}}}


{{{2a+7x=9}}}  Equation A


Also {{{a+2x=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.


*[invoke linear_substitution "a", "x", 2, 7, 9, 1, 2, 4 ]


So a={{{10/3}}} and x={{{1/3}}}


So sequence is:  {{{10/3}}}, {{{11/3}}}, {{{4}}}, {{{13/3}}}, {{{14/3}}}, {{{5}}}, {{{16/3}}}, {{{17/3}}}.


Check:  The third term is {{{4}}} and the sum is {{{(10+11+12+13+14+15+16+17)/3=36}}} 


Step 6.   ANSWER:  The sequence is {{{10/3}}}, {{{11/3}}}, {{{4}}}, {{{13/3}}}, {{{14/3}}}, {{{5}}}, {{{16/3}}}, {{{17/3}}}.


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