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3 years ago

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

Mathematics

1 answer:

Alja [10]3 years ago

8 0

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.

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4 years ago

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3 years ago

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4 0

4 years ago

A bicycle store costs $2400 per month to operate. Thee store pays an average of $60 per bike. The average selling price of each

n200080 [17]

Answer:

The number of bicycle that store sell each month to break even is 13 bikes .

Step-by-step explanation:

Given as :

The operation cost of bicycle store = $2400

The cost of payment by store at average rate = $60 per bike

The average selling price of each bike = s.p = $120 per bike

Let The number of bicycle that store sell each month to break even = n bikes

According to question

The operation cost of bicycle store = (cost of payment by store at average rate + average selling price of each bike ) × number of bicycle that store sell each month to break even

i.e ($60 per bike + $120 per bike) × n bikes = $2400

Or, ($180 per bike) × n bikes = $2400

∴ 180 n = 2400

Or, n = $\dfrac{2400}{180}$

i.e n = 13.333 ≈ 13

So, The number of bicycle that store sell each month to break even = n = 13 bikes

Hence, The number of bicycle that store sell each month to break even is 13 bikes . Answer

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4 years ago