Question

if the pth term of an ap is q and q term of an ap is p prove that its nth term is p + q - n​

Answer 1

Step-by-step explanation:

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Answer 2

Your question,

if the pth term of an AP is q and qth term of an AP is p.Prove that nth term of that AP is p+q-n

Step-by-step explanation:

Given,

pth term = q

which means

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

qth term = p

which means

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

Now on subtracting both (1) and (2),

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

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

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

(p-q)d=q-p

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

Now,put d value in eq(1)

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

a-p+1=q

a=p+q-1

As per the question,

an=a+(n-1)d........you must be knowing this

an=p+q-1+(n-1)(-1)

an=p+q-1-n+1

an=p+q-n

Hence proved

Formulas used,

an=a+(n-1)d

where a= first term

d=common difference

n=nth term