Question

How
many multiples of 4 lie between 15 to 735?
find their sum?

Answer 1

$\underline{\boxed{\bold{Question}}}$

↠ How  many multiples of 4 lie between 15 to 735?

↠ Find their sum?

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$\underline{\boxed{\bold{Important\;information}}}$

↠ An arithmetic progression (AP) or arithmetic sequence is series of numbers such that difference between two numbers is constant and is referred as common difference.

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$\underline{\boxed{\bold{Important\;Formulas}}}$

• nth term of AP is given by,

$\implies A_n = a + (n-1)d$

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• Sum of "n" terms AP is given by,

$\implies S_n = \frac{n}{2}[2a + (n-1)d]$

$\implies S_n = n \times (\frac{First\;Term + Last\;term}{2} )$

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

AP = 16, 20, 24, 28, 32 ............... 728, 732

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→ First Term = 16

→ Last term = 732

→ Common difference = 4

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To find total numbers of multiple, we need to find which term is 732 in given AP.

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$:\implies A_n = a + (n-1)d$

$:\implies 732 = 16 + (n-1)4$

$:\implies 716 = (n-1)\times 4$

$:\implies (n-1) = 179$

$\boxed{:\implies n = 180}$

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Now let's find sum by given formula,

$:\implies S_n = n \times (\frac{First\;Term + Last\;term}{2} )$

$:\implies S_n = 180 \times (\frac{16+732}{2} )$

$:\implies S_n = 90 \times 748$

$\boxed{:\implies S = 67320}$

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$\boxed{\boxed{\bold{\therefore Total\; number\;of\;multiples\;=180}}}$

$\boxed{\boxed{\bold{\therefore Sum\;of\; this\;multiples\;=67320}}}$

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Hope this helps u.../

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