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if 9 times the 9^(th) term of an ...

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

A

`0`

B

`22`

C

`198`

D

`220`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the first term be a and common difference be d.
Acording to the question , `9,T_(9) =13.T_(13)`
`implies 9(a+8d)=13(a+12d)`
`implies 9a+72 d=13a + 156 d`
`implies (9a-13a )=156 d -72d`
`implies -4a=84d`
`implies a=-21d`
`implies a+21d=0`
` therefore "22nd term i.e., " T_(22) =[a+21d]`
`T_(22) =0` [ using Eq.(i) ]
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