Question

The $9^{th}$ term of an A.P. is 449 and ${449}^{th}$ term is 9 The term which is equal to zero is

• A. ${501}^{th}$
• B. ${502}^{th}$
• C. ${508}^{th}$
• D. None of these

Answer 1

The correct option is D None of these

Let a and d be the first term and common difference of A.P. respectively.
$nth$ term of A.P.,$a_n=a+(n-1)d$
Given,$a_9=449$
$449=a+(9-1)d$
$449=a+8d$ ...(1).
Given,$a_{449}=9$
$a+(449-1)d=9$
$a+448d=9$ ...(2)
Solving (1) and (2), we get
d = -1
When d = -1, we get
$a+8(-1)=449$
$a=449+8=457$
Let m
th term of the A.P. be 0.
$a_m=0$
$a+(m-1)d=0$
$457+(m-1)(-1)=0$
$457+1-m=0$
$458=m$
$m=458$
Thus, 458
th term of the given A.P. is 0
Answer (D) None of these