Question

the sum of pth term of ap isq andqth term of ap is p find [p+q]th term of ap

Answer 1

Refer to the attachment for your solution









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Answer 2

Here your answer goes

Given ,

P th term of an AP = q  

q th term of an AP = P

To Find  :-

[ p + q ] th term of an AP

Solution :-

We know that ,

Formula for $a_{n} = a+( n-1) *d$

So , For pth term = $a +(n -1)* d$

⇒ q = a + ( P - 1 ) * d ------->>>> 1

Similarly ,

⇒ P = a + ( q - 1 ) * d ---------->>>> 2

From (1) and (2)

$a + ( P - 1 ) * d \\\\ a +( q - 1 ) * d \\===============\\Pd - qd = q - p$

⇒ d ( p -q ) = - ( p - q )

⇒ d = -1

Substitute the value of d in equation (1)

q = a + ( P - 1 ) * d

⇒ q  =  a + ( p - 1 ) * (-1)

⇒ q =  a - p + 1

⇒ a = q + p - 1

⇒ a ( p + q ) = a + ( n - 1 ) * d

⇒ a (p + q - 1 - p - q + 1 )

⇒ a [ p + q ] = 0

Therefore , [ p + q ] th term of an AP = 0

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