SOLUTION: The first term of an arithmetic progression is -8.The ratio of the 7th term to the 9th is 5:8. Calculate the common difference

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Question 1132681: The first term of an arithmetic progression is -8.The ratio of the 7th term to the 9th is 5:8. Calculate the common difference
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
an arithmetic progression is:
a%5B1%5D, a%5B1%5D+%2B+d, a%5B1%5D+%2B+2d+, a%5B1%5D+%2B+3d+,.........and so on.
Thus nth term of an AP series is
a%5Bn%5D+=+a+%2B+%28n+-+1%29+d, where a%5Bn%5D+=+n%5Bth%5D term and a%5B1%5D+= first term. and d is common difference = a%5Bn%5D+-+a%5Bn-1%5D

given:
a%5B1%5D=-8
+a%5B7%5D+%2F+a%5B9%5D+=5%2F8
since +a%5B7%5D=+a%5B1%5D+%2B+%287-1%29d+ and +a%5B9%5D=+a%5B1%5D+%2B+%289-1%29d+, we have

%28-8%2B%287-1%29d%29%2F%28-8%2B%289-1%29d%29=5%2F8
%28-8%2B6d%29%2F%28-8%2B8d%29=5%2F8
%284+-+3d%29%2F%284+-+4+d%29+=+5%2F8
d=3

+-8, -8%2B3, -8+%2B+2%283%29, -8%2B+3%283%29+,-8%2B4%283%29,-8%2B5%283%29, -8%2B6%283%29, -8%2B7%283%29, -8%2B8%283%29
so, your sequence is:
+-8,+-5, -2, 1, 4, 7, 10, 13, 16
chech the ratio of the 7th term to the 9th if it is 5%3A8
%2810%2F16%29=5%2F8
%285%2F8%29=5%2F8-> confirmed


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The first term of an arithmetic progression is -8.The ratio of the 7th term to the 9th is 5:8. Calculate the common difference 


We then get: matrix%281%2C3%2C+%28-+8+%2B+6d%29%2F%28-+8+%2B+8d%29%2C+%22=%22%2C+5%2F8%29

8(- 8 + 6d) = 5(- 8 + 8d) ------- Cross-multiplying

- 64 + 48d = - 40 + 40d

48d - 40d = - 40 + 64

8d = 24

d, or common difference = highlight_green%28matrix%281%2C3%2C+24%2F8%2C+%22=%22%2C+3%29%29