Question

If the pth term of an AP is q and its qth term is p, then show that its (p + q)th term is zero.​

Answer 1

Step-by-step explanation:

Hope this will help you

Answer 2

Answer:

(p+q)th term = 0

Step-by-step explanation:

first term = a

common difference = d

formula for nth term = a+(n-1)d

pth term = a+(p-1)d = q ---- 1

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

subtract the two equations

1 - 2  

a+(p-1)d -[ a+(q-1)d] = q-p

a+pd-d-[a+qd-d] = q-p

a+pd-d-a-qd +d = q-p

pd-qd = q-p

d(p-q) = q-p

d = q-p/p-q

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

d = -1

substitute d = -1 in equation 1

a+(p-1)*-1 = q

a + -p +1 = q

a = p+q-1

(p+q)th term = a+(p+q-1)d

                     = p+q-1 +(p+q-1)*-1      ( a= p+q-1 , d = -1)

                     = p+q-1 -p-q +1 = 0