Question

A student named Akash is observing birds flying in the sky at the evening time. Birds are flying in the pattern like 1 in the first row, 3 in the second, 5 in the third and so on ..........
Making total 20 rows as per the figure given below, find out the total number of birds.

• A. 39
• B. 400
• C. 40
• D. 200

Answer 1

The correct option is B 400

Number of birds in first row $=1$
Number of birds in second row $=3$
Number of birds in third row $=5$ and so on......

So, the series $1,3,5,7,.........$ is making arithmetic progression
Thus, $a=1$
Common difference $d=3-1=2=5-3$
There are $20$ terms $⟹n=20$
Now, $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$=\frac{20}{2}\left[2\right(1)+(20-1\left)2\right]$
$=10[2+38]$
$=10\times 40$
$=400$

Hence, the total no. of birds is $400$.