Home
Class 10
MATHS
If m times the mth term of an AP is equa...

If m times the mth term of an AP is equal to n times its nth term, then show that (m + n)th term of an AP is zero.

Text Solution

Verified by Experts

Let a be the first term d be the common difference of the given AP. Then,
`T_(m) = a + (m-1)d "and" T_(n) = a + (n-1)d.`
Now, `(m * T_(m)) = (n * T_(n)) rArr m * {a+ (m-1)d} = n * {a +(n-1)d}`
`rArr a * (m-n) + {(m^(2) -n^(2)) - (m-n)} * d = 0`
`rArr (m-n) * {a + (m +n -1)}d.`
`rArr (m-n) * T_(m+n) = 0`
`rArr T_(m+n) = 0 [because (m-n) ne 0].`
Hence, the (m+n)th term is zero.
Promotional Banner

Similar Questions

Explore conceptually related problems

If m xx the mth term of an AP is equal to n xx its nth term,then show that (m+n) th term of an AP is zero.

If m times the m^(th) term of an A.P. is equal to n times its n^(th) term , then show that (m+n)^(th) term of the A.P. is zero .

If m times the mth term of an A.P. is equal to n times its nth term, find (m + n) th term of the A.P.:

If 9 times the 9th term of an AP is equal to 13 times the 13th term, show that its 22 nd term is 0.

If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be

if 9 times the 9 th term of an AP is equal to 13 times the 13 th term , then the 22 nd term of the AP is

If m xx the m^(th) term of an A.P.is equal to n xx its n^(th) term,show that the (m+n)^(th) term of the A.P.is zero.

If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.

If 6 times the 6^(th) term of an A.P, is equal to 9 times the 9^(th) term, show that its 15^(th) term is zero.