Posted by **Hussain** on Tuesday, May 14, 2013 at 1:45pm.

there are n arithmetic means between 5 and 32 such that the ratio between the 3rd and 7th means is 7:13,find the value of n.

- arithmetic -
**Reiny**, Tuesday, May 14, 2013 at 3:07pm
the sequence would be

5 , 5+d , 5+2d , 5+3d , .... , 5 + (n-2)d , 32

for n+2 terms

3rd mean = 4th term = a+3d

7th mean = 8th term = a + 7d

but a = 5

(5+3d)/(5+7d) = 7/13

35 + 49d = 65 +39d

10d = 30

d = 30/10 = 3

so a + ((n+2)-1)d = 32

5 + (n+1)(3) = 32

3n+3 = 27

3n = 24

n = 8

check:

5 **8 11 14 17 20 23 26 29** 32

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