Question

Find the average of first 30 multiples of 8?​

Answer 1

Answer:

124

Step-by-step explanation:

Number*(n+1)/2.

So it's,

= 8 * (30+1)/2,

= 8 * 31/2,

= 4 * 31.

So, 124 is the answer

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Answer 2

Given:

• To find average of first 30 multiples of 8.

Concept Used:

• We will use formula of AP to find sum of first 30 multiples of 8.
• Then we will divide it by total 30 terms i.e. 30 by the sum found to find out the average.

Answer:

Here we have to find out the average of first 30 multiples of 8 .

So , sum of first 30 multiples would be ,

☞ $\sf{\underbrace{8 + 8\times2 + 8\times3 + 8\times4 +...............8\times29. }}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:(30\:terms)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$

This can be written as ,

☞ 8+(8+8)+(16+8)+(24+8).............(224+8).

From above its clear that the above progression is Arithmetic Progression (AP) since 8 is added to each terms .

And , Sum of n terms of an AP is given by ,

$\large{\underline{\boxed{\red{\sf{\hookrightarrow S_{n}=\dfrac{n}{2}[2a+(n-1)d]}}}}}$

where ,

• ☞$\sf{S_{n}}$ is the sum of series.
• ☞n is number of terms.
• ☞d is Common Difference.
• ☞a is first term.

Here ,

1. ☞a = 8
2. ☞n = 30 .
3. ☞d = 8 .

Using above formula,

$\sf{\implies S_{n}=\dfrac{30}{2}[2\times8+(30-1)\times8]}$

$\sf{\implies S_{n}=15[16+29\times8]}$

$\sf{\implies S_{n}=15[16+232]}$

$\sf{\implies S_{n}=15\times248}$

${\underline{\boxed{\red{\sf{\leadsto S_{n}= 3720}}}}}$

$\rule{200}4$

Now , formula of average is;

$\large{\underline{\boxed{\red{\sf{\hookrightarrow Average=\dfrac{Sum\:of\:terms}{Total\: number\: of\:terms}}}}}}$

$\sf{\implies Average =\dfrac{3720}{30}}$

${\underline{\boxed{\red{\sf{\leadsto Average=124}}}}}$

Hence the average of first 30 multiples of 8 is 124.