Home
Class 12
MATHS
If 100 times the 100th of an A.P. with n...

If 100 times the 100th of an A.P. with non-zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is `:`

A

150 times its 50th term

B

150

C

zero

D

-150

Text Solution

Verified by Experts

The correct Answer is:
C
Let a be the first term and d be the common difference. Then,
`100T_(100)=50T_(50)`
`implies 100(a+99d)=50(a+49d)`
`implies 2(a+99d)=(a+49d) implies a+149d=0`
`:. T_(150)=0`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the common difference of the AP in which 18th term is 10 less than the 20th term.

If 29th term of an A.P is twice its 19th term, then the 9th term is

In the A.P., the common difference is 3, first term is 1, then its tenth term is:

If 9 times the 9th term of an A.P. is equal to 13 times the 13^(th) term, then 22nd term of the A.P. is :

In an A.P., 7 times the 7th term is equal to 11 times 11th term. Find the 18th term of the A.P.

In a certain A.P., 5 times the 5th term is equal to 8 times the 8th terms then find its 13th term.

The first n^(th) term of a AP is given by

In a sequence of 21 terms the first 11 terms are in A.P. with common difference 2. and the last 11 terms are in G.P. with common ratio 2. If the middle tem of the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is

If 5 times of the 5^(th ) element of an A.P is equal to 9 times the 9^(th) element, then 14^(th) element of the A . P is