Home
Class 12
MATHS
If the pth term of an A.P. is q and the ...

If the pth term of an A.P. is q and the qth term isp, then find its rth term.

Text Solution

Verified by Experts

The correct Answer is:
p+q-r

a+(p-1)d=q and a+(q-1)d=p
`rArr(p-q)d=q-p`
`rArr d=-1`
`T_(r)=a+(r-1)d=a+(p-1)d+(r-p)d`
`=q-(r-p)=p+q-r`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.3|9 Videos
  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.4|13 Videos
  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.1|3 Videos
  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos
  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

If the pth term of an A.P. is q and the qth term is p , then find its rth term.

If the common difference of an A.P. is – 3 and the 18th term is – 5, then find its first term.

if the Pth term of an A.P. is q and qth term is P.Then show that the nth term is p+q-n

If the first term of an A.P. is – 18 and its 10th term is zero, then find its common difference.

If the (p+q)th term of a G.P. is a and (p-q)th term is b, determine its pth term.

The pth term of an A.P. is a and qth term is bdot Then find the sum of its (p+q) terms.

If the seventh term of an A.P. is 1/9 and its ninth term is 1/7 , find its 63rd term.

The rth terms of an A.P is n and it's nth term is r, show that its mth term is r+n - m.

The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.

The mth term of a H.P is n and the nth term is m . Proves that its rth term is (mn)/r