1.IF Pth term of an A.P is q and qth tem of an AP is p then prove that (p+q) term is 0

Question

vikas askiitian expert · Answer

let a & d are the first term & common differnece respectively then

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

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

1-2

q-p = (p-q)d

d=-1

now

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

putting value of a from eq 1

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

=0

Fawz Naim · Answer

The pth term of an AP is = a+(p-1)d

where a is the first term of the AP and d is the common difference

as pth term is equal to q therefore q=a+(p-1)d .....1

similarly qth term is equal to p

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

solve the two equations to get the value of a and d. It will come

a=p+q-1

d=-1

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

put the values of a and d

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

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

=0

Kushagra Madhukar · Answer

Dear student, Please find the attached solution to your problem. Let the first term of A.P. = a and common difference = d pth term → a + (p-1)d = q – (1) qth term → a + (q-1)d = p – (2) eq(1) – eq(2) (p-q)d = q-p or, d = -1 putting d = -1 in eq(1) we get, a = p+q-1 Now, (p+q)th term → a + (p+q-1)d = p+q-1 - (p+q-1) = 0 Hope it helps. Thanks and regards, Kushagra

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

1.IF Pth term of an A.P is q and qth tem of an AP is p then prove that (p+q) term is 0

1.IF Pth term of an A.P is q and qth tem of an AP is p then prove that (p+q) term is 0

3 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Algebra

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship