if pth term of AP is q and qth term of Ap is p prov that nth term is p+q-n
pranav , 8 Years ago
Grade 10
Algebra> if pth term of AP is q and qth term of Ap...
3 Answers
Harsh Patodia
Last Activity: 8 Years ago
ap = q = a + (p-1)d (1)
aq =p = a + (q-1)d (2)
(1) – (2)
q-p = (p-q)d
d= -1
Substituting d in (1)
a= p+q -1
an = a+(n-1)d = p+q-1 + (n-1)(-1)
an = p+q-1 -n +1 = p+q-n
Nikhil kumar
Last Activity: 8 Years ago
Let the A.P. be given by
q = a + (p -1)d ... ( 1 )
p = a + (q -1)d ... ( 2 )
Subtracting ( 2 ) from ( 1 ),
q - p = (p - q)d => d = -1
Putting d = -1 in ( 1 ), a = p + q - 1
nte term = a + (n - 1)d
Substituting the values of a and d,
nth term = p + q - 1 + (n -1)(-1) = p + q – n.
q = a + (p -1)d ... ( 1 )
p = a + (q -1)d ... ( 2 )
Subtracting ( 2 ) from ( 1 ),
q - p = (p - q)d => d = -1
Putting d = -1 in ( 1 ), a = p + q - 1
nte term = a + (n - 1)d
Substituting the values of a and d,
nth term = p + q - 1 + (n -1)(-1) = p + q – n.
SREEKANTH
Last Activity: 8 Years ago
pth term of arithematic progression pth=a+(p-1)d qth term of arithematic progression qth=a+(q-1)d nth term of ap is=a+(n-1
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