Home
Class 10
MATHS
In a given A.P.. If the pth term is q a...

In a given A.P.. If the `p`th term is `q` and `q`th term is `p` then show that `n` th term is `p+q-n`

Text Solution

Verified by Experts

Let a be the first term and d be the common difference of the given AP. Then,
`T_(p) = a + (p-1)d "and" T_(q) = a + (q-1)d.`
Now, `T_(p) = q "and" T_(q) = p` (given).
`therefore a + (p-1)d =q " "...(i)`
`"and" a+ (q-1)d = p " "...(ii)`
On subtracting (i) from (ii), we get
`(q-p)d = (p-q) rArr d = -1.`
Putting d = -1 in (i), we get a = (p+q-1).
Thus, a = (p+q-1) and d = -1.
`therefore "nth term" = a + (n-1)d = (p+q-1) + (n-1) xx (-1)`
= p+q - n.
Hence, nth term = (p+q -n).
Promotional Banner

Similar Questions

Explore conceptually related problems

If the p^(th) term of an A.P is q and q^(th) term is p, prove that its n^(th) term is (p+q-n)

If in an A.P.the pth term is q and (p+q)^(th) term is zero then the q^(th) term is -p b.p c.p+q d.p-q

If (2p)th term of a G.P is q^2 and (2q)th term is p^2 then (p+q)th term is

If the p^(th) term of an A.P.is q and the q^(th) term is p, prove that its n^(th)term is(p+q-n)

If in an AP, the q^(th) term is p and (p+q)^(th) term is zero ,then find p^(th) term.

In an A.P if m^( th ) term is n and the n^( th ) term is m ,where m!=n ,find the p^(th term.

(i) The 3rd term of an A.P. is 1 and 6 th term is -11. Determine its 15th term and rth term. (ii) In an A.P. , the third term is p and the fourth term is q, find the 10 th term and the general term.