Question

Find the sum of the given arithmetic series. 24 + 48 + 72 + 96 +...+ 480

Answer 1

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, $a_n=480$

Let there are n terms in the AP.

So,

$a_n=a+(n-1)d\\\\480=24+(n-1)24\\\\480=24+24n-24\\\\n=20$

There are 20 terms in the series. The sum of 20 terms is :

$S_{20}=\dfrac{n}{2}(2a+(n-1)d))\\\\=\dfrac{20}{2}\times (2(24)+19(24))\\\\=5040$

So, the sum of the given arithmetic series is equal to 5040.