Question

If $p^t^h$ term of an AP is $\frac{1}{q}$ and $q^t^h$ term is $\frac{1}{p}$ then find the sum of $pq$ terms. Following is the attached file{just, in case}

Answer 1

EXPLANATION.

• GIVEN

Pth term of an Ap = 1/q

qth term of an Ap = 1/p

FIND THE SUM OF PQ TERM.

according to the question,

Pth = a + ( p - 1 ) d = 1/q ..... (1)

qth = a + ( q - 1 ) d = 1/p ..... (2)

subtracting equation (1) and (2)

we get,

( p - q) d = ( p - q) / pq

d = 1/pq

put the value of d = 1 / pq in equation (1)

we get,

a + ( p - 1 ) 1 / pq = 1/q

a + p/pq - 1 / pq = 1/q

a = 1 / pq

formula of sum of n terms

sum of n term = n / 2 ( 2a + ( n - 1 ) d)

Sum of pq term =

PQ / 2 [ 2 ( 1/PQ ) + ( PQ - 1 ) 1/PQ]

PQ / 2 [ 2 / PQ + PQ / PQ - 1 / PQ ]

PQ / 2 [ 1 / PQ + 1 ]

PQ / 2 [ 1 + PQ / PQ ]

1/2 [ PQ + 1 ]

Therefore,

sum of pq terms of ap = 1/2 [ pq + 1 ]