SOLUTION: The terms 5 + x, 8, and 1 + 2x are consecutive terms in an arithmetic sequence. Determine the value of x and state the three terms.

Algebra ->  Sequences-and-series -> SOLUTION: The terms 5 + x, 8, and 1 + 2x are consecutive terms in an arithmetic sequence. Determine the value of x and state the three terms.      Log On


   

Question 935824: The terms 5 + x, 8, and 1 + 2x are consecutive terms in an arithmetic sequence. Determine the value of x and state the three terms.
Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first term is 5+%2B+x,
second term is 8, and
third term is 1+%2B+2x
you know that between each term is same difference:
8-%285+%2B+x%29 is same as %281+%2B+2x%29-8
make it equal and solve for x
8-%285+%2B+x%29=%281+%2B+2x%29-8
8-5+-x=1+%2B+2x-8
3+-x=2x-7
3+%2B7=2x%2Bx
10=3x
10%2F3=x
3%2B%281%2F3%29=x
first term is 5+%2B+x=5%2B3%2B%281%2F3%29=8%2B%281%2F3%29, =>8%281%2F3%29
second term is 8, and
third term is 1+%2B+2x=1%2B2%283%2B%281%2F3%29%29=1%2B6%2B2%2F3%29=7%2B%282%2F3%29 =>7%282%2F3%29


Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Difference between consecutive terms is constant.

8-5-x=d and 1%2B2x-8=d.

3-x=2x-7
10=3x
x=10%2F3


5%2B10%2F3
15%2F3%2B10%2F3
highlight%2825%2F3%29
8%261%2F3


1%2B2%2810%2F3%29
3%2F3%2B20%2F3
highlight%2823%2F3%29
7%262%2F3