Question

You visit the swimming pool and drop a stone off the edge of a cliff. The distance the stone will fall is $16$ meter the first second, $48$ meter the next second, $80$ meter the third second, and so on in an arithmetic sequence. What is the total distance the stone will fall in $6$ seconds?

• A. $576$
• B. $564$
• C. $578$
• D. $589$

Answer 1

The correct option is A $576$

The sequence is $16,48,80.....$
$a=16,d=32$
First find the common difference:
$a_n=a_1+(n-1)d$
$a_6=16+(6-1)32$
$=16+5\times 32$
$a_6=176$
We know that, $S_n=\frac{n}{2}$ [First term $+$ Last term]
$=\frac{6}{2}[16+176]$
$=3\left[192\right]$
$S_6=576$
Hence, the total distance the stone will fall in $576$ in $6$ seconds.