###
**The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is**

A. 50th
B. 502th
C. 508th
D. None of these
**Answer: Option D**

## Show Answer

Solution(By Apex Team)

$\begin{array}{l}\begin{aligned}a_n&=a+(n-1)d\\
a_9&=449\\
&=a+(9-1)d\\
&=a+8d\ldots\ldots(1)\\
a_{449}&=9\\
&=a+(449-1)d\\
&=a+448d\ldots(2)\end{aligned}\\
\text{ Subtracting }\\
440d=-440\\
\begin{array}{l}\Rightarrow d=\frac{-440}{440}=-1\\
\text{ and }a+8d=449\\
\Rightarrow a\times8\times(-1)=449\\
\Rightarrow a=449+8=457\\
\therefore0=a+(n-1)d\\
\Rightarrow0=457+(n-1)(-1)\\
\Rightarrow0=457-n+1\\
\Rightarrow n=458\\
\therefore458^{\text{th }}\text{ term }=0\end{array}\end{array}$

## Related Questions On Progressions

### How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22B. 25

C. 23

D. 24

### Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5B. 6

C. 4

D. 3

### Find the 15th term of the sequence 20, 15, 10 . . .

A. -45B. -55

C. -50

D. 0

### The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600B. 765

C. 640

D. 680