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If a, b, c are in A.P. and p is the A.M. between a and b and q is the A.M. between b and c, then
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a
a is the A.M. between p and q
b
b is the A.M. between p and q
c
c is the A.M. between p and q
d
None of these
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Correct option is B
∵a,b,c are AP., ∴ 2b=a+c (1)∵ p is the A.M. between a and b∵ p=a+b2 (2)∵ q is the A.M. between b and c∵ q=b+c2 (3)Adding Eq. (2) and (3)p+q=a+b2+b+c2=a+c+2b2=2b+2b2=2b [Using (1)]∴ 2b=p+q or b=p+q2Hence, b is the A.M. between p and q.Similar Questions
Between 1 and 31 are inserted M arithmetic means so that the ratio of the 7th and (M - 1) th means is 5:9, then the value of m is
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