Answer:
5040
Step-by-step explanation:
The given series is :
24 + 48 + 72 + 96 +...+ 480
The first term, a= 24
Common difference, d = 24
The last term, [tex]a_n=480[/tex]
Let there are n terms in the AP.
So,
[tex]a_n=a+(n-1)d\\\\480=24+(n-1)24\\\\480=24+24n-24\\\\n=20[/tex]
There are 20 terms in the series. The sum of 20 terms is :
[tex]S_{20}=\dfrac{n}{2}(2a+(n-1)d))\\\\=\dfrac{20}{2}\times (2(24)+19(24))\\\\=5040[/tex]
So, the sum of the given arithmetic series is equal to 5040.
