if p,q,r are three consecutive terms of an AP then q will be _____ of p and r. options mean, median,mode,sum
Answers
If p,q,r are three consecutive terms of an A.P, then q will be the mean of p, r
- Arithmetic progression: The progression which is in the form of a, a+2d, a+3d,..... is known as arithmetic progression with first term a and the common difference d
- If p,q,r are three consecutive terms in A.P, then the value of q can be written as the average of p and r i.e.,
q = (p+r)/2
- From the above relation it is clear that q will be the mean of p and r
Given : p,q,r are three consecutive terms of an AP
To find : q will be _____ of p and r.
Solution:
p,q,r are three consecutive terms of an AP
AP - arithmetic progression
a , a + d , a + 2d ,......................
d is the common difference between consecutive terms
p , q , r are consecutive terms
hence
q = p + d
r = q + d = p + d + d = p + 2d
q = p + d
=> 2q = 2(p + d)
=> 2q = 2p + 2d
=> 2q = p + p + 2d
=> 2q = p + r
=> q = (p + r)/2
Hence q is the mean of p & r
also q lies between p & r in a order and is middle term
Hence q is median of p , q & r also
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