Question

IF (p+q)th term is m of an ap and (p-q)th term is n then pth term is

Answer 1

Given:

=> a+(p+q-1)d=m

=> a+(p-q-1)d=n

To Find:

=> To find pth term is

Solution:

=> a+(p+q-1)d=m

=> a+(p-q-1)d=n

=> subtracting both the equations we get

a+(p+q-1)d=m

a+(p-q-1)d =n

(-) (-) (+)(+) (-)

——————–——

( 2q)d = m-n

d = m-n/2q

puting [ d = m-n/2q] in the first equation.

we get,

=> a+(p+q-1)(m-n)/2q=m

=>a+(p-1)(m-n)/2q + q(m-n)/2q =m

therefore ,

=> a+(p-1)d +(m-n)/2 =m

so,

=> a+(p-1)d =m-(m-n)/2

=(2m-m+n)2

=> a+(p-1)d =(m+n)/2

Since a+(p-1)d is the form of the pth term therefore,

pth term = (m+n)/2

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