Math, asked by RakshaDeeku2549, 1 year ago

If the pth term of an ap is q and the qth term is p , prove that its rth term is p + q - r

Answers

Answered by Jindalnayan
138
Hence proved. (so simple)
Attachments:
Answered by isyllus
98

Answer:

Hence Proved, rth term of the AP is p+q-r

Step-by-step explanation:

If the pth term of an AP is q and the qth term is p

Let first term of AP is a and common difference is d

a_p=q

a+(p-1)d=q

a+(q-1)d=p

Solve for a and d

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

d=-1

Put d=-1 into a+(p-1)d=q

a-(p-1)=q

a=p+q-1

We need to find rth term of same AP where a=p+q-1 and d=-1

a_r=a+(r-1)d

a_r=p+q-1-1(r-1)

a_r=p+q-r-1+1

a_r=p+q-r

Hence proved, rth term of the AP is p+q-r

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