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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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Answer:

(1)

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Alice: $y = 2x +1$

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(3) y intercept

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$b = 1$ --- For Alice

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(5) No solution

(6) No

Step-by-step explanation:

Given

$x = loaves$

$y = amount$

Solving (1): Complete the equation.

For Karen:

$m = 2$ --- the rate

$b = 3$ --- additional spendings

For Alice:

$m = 2$ --- the rate

$b = 1$ --- additional spendings

The general equation is;

$y = mx +b$

For Karen, it becomes

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For Alice, it is:

$y = 2x +1$

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In (1), we have:

$m = 2$ --- the rate (for both Karen and Alice).

This rate implies the slope.

Hence, the slope is 2

(3): The y intercept.

The additional spendings in (1) means the y intercept.

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$b = 1$ --- For Alice

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