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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

Grade:12

3 Answers

vikas askiitian expert
509 Points
10 years ago

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
37 Points
10 years ago

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
askIITians Faculty 629 Points
one year ago
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

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