Question

A singer sang $100$ songs on the first day, $90$ songs on the second day and $80$ songs on the third day, and so on in an arithmetic sequence. How many songs did the singer sing in a week?

• A. $490$
• B. $563$
• C. $575$
• D. $543$

Answer 1

Answer: (A)

$490$

The sequence is $100,90,80.....$
$a=100,d=-10$
First find the common difference:
$a_n=a_1+(n-1)d$
$a_7=100+(7-1)(-10)$
$=100-60$
$a_7=40$
We know that, $S_n=\frac{n}{2}$ [First term $+$ Last term]
$=\frac{7}{2}[100+40]$
$=3.5\left[140\right]$
$S_{17}=490$
Hence, the singer will sing $490$ songs.