Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

State True/False.

If the pth term of an AP is q and its q th term is p then its $(p + q)$ th term is zero.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that

p t h

term of AP is q and

q t h

term of AP is p.
Let first term be a and common difference be d.
So, from first given condition: h

∴ a p = q

Formula for the

n t h

term:

a n = a + n − 1 × d

Applying the formula of nth term of A.P.

∴ a + (p − 1) d = q

-----(1)
Now, from second given condition:

∴ a q = p

Applying the formula of nth term of A.P.

∴ a + (q − 1) d = p

------(2)
Subtract equation (1) from equation (2):

∴ a + (q − 1) d − {a + (p − 1) d} = p − q ⇒ a + q d − d − {a + p d − d} = p − q ⇒ a + q d − d − a − p d + d = p − q ⇒ q d − p d = p − q

⇒ d (q − p) = p − q ⇒ d (q − p) = − (q − p) ⇒ d = − (q − p) q − p ⇒ d = − 1

Put the value of d in equation (1):

∴ a + (p − 1) × (− 1) = q ⇒ a − p + 1 = q ⇒ a = p + q − 1

Applying the formula of

n th

term of AP for

a p + q

∴ a p + q = (p + q − 1) + (p + q − 1) (− 1) ⇒ a p + q = (p + q − 1) − (p + q − 1) = 0

Therefore, the

(p + q) t h

term is 0.
Thus, the given statement is true.
Hence, option (1) is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!