if the pth term of an A.P is q and the qth term is p, prove that its nth term is (p+q-n)

Share with your friends

Shen Darlene answered this

Let the A.P. be given by
a, a+d, a+2d, a+3d,.....
q = a + (p -1)d ... ( 1 )
p = a + (q -1)d ... ( 2 )

Subtracting ( 2 ) from ( 1 ),
q - p = (p - q)d => d = -1
Putting d = -1 in ( 1 ), a = p + q - 1
nte term = a + (n - 1)d
Substituting the values of a and d,
nth term = p + q - 1 + (n -1)(-1) = p + q - n.

View Full Answer

Raghuraman answered this

a + (p - 1)d = q

a + (q - 1)d = p

solving, a = q(q - 1) - p(p - 1)/(q - p) = q² - p² + p - q/ (q - p) = q +p - 1

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

nth term = a + (n - 1)d

= q + p - 1 - n + 1

= q + p - n

thumbs up plzzzzz

Rushia answered this

thanks

Rushia answered this

thanks dear thanks a lot

Vartika answered this

according to question,

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

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

by subtracting 2 from 1 we get,

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

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

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

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

so,d = -1 ......3

putting value of d in 1,we get,

a+(p-1) -1=q

a-p+1 = q

so,a= (q+p-1) ......4

now,we know that,

t_n = a + (n-1)d

by putting the value of a and d,we get,

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

=p+q-1-n+1

=(p+q-n).....proved!

good luck... :)

Harsh Veer answered this

Good

Naman answered this

In an ap proove that d=Sn-2Sn-1+Sn-2

Nikshep Nikshep answered this

i cant understand

Soumili Paul answered this

Its really interesting.

Sarayu answered this

Let first term be a and common difference be d.

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

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

(ii) - (i) gives

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

(i) gives? a = q - (p-1)d = q - (p-1)(-1) = q + p - 1

Hence,

nth term = a + (n-1)d = q + p -1 + (n-1)(-1) = q + p -1 + n +1 = p + q - n

-4

Tanmay Jha answered this

Toes up!!

-6

Naveen answered this

thanks vartika.

S Raj answered this

Rahe de

Sudhantttttttttt answered this

How r u?

Anurag answered this

thank u vartika dear

Rishika Singh answered this

how do u ask question in meritnation. i know how to answer but idk how to ask pls help. i will be following dis question.

Melophile answered this

Hope it will help!!!👍👍👍

Arun Virat answered this

Funny answer

Aditi answered this

Thamk you varti ka😘🙏🙏🙏

-8

Aditya answered this

according to question, a + (p-1)d = q ....1 and a+(q-1)d = p ....2 by subtracting 2 from 1 we get, (p-1)d - (q-1)d = q-p d((p-1)-(q-1)) = (q-p) d(p-1-q+1)= (q-p) d(p-q) = (q-p) so,d = -1 ......3 putting value of d in 1,we get, a+(p-1) -1=q a-p+1 = q so,a= (q+p-1) ......4 now,we know that, tn = a + (n-1)d by putting the value of a and d,we get, tn =(p+q-1) + (n-1)-1 =p+q-1-n+1 I hope this is helpful for you =(p+q-n).....proved!

Gaganjain answered this

Here it is⬇️⬇️

Zaneta answered this

Let first term be a and common difference be d.
pth term = a + (p-1)d = q -----(i)
qth term = a + (q-1)d = p -----(ii)
(ii) - (i) gives
(q - p)d = p - q or d = -1
(i) gives a = q - (p-1)d = q - (p-1)(-1) = q + p - 1
Hence,
nth term = a + (n-1)d = q + p -1 + (n-1)(-1) = q + p -1 + n +1 = p + q - n