Question

Find the sum of n terms of the AP.,+d.+2d.. +(n-1)d
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Answer 1

$\Huge{\underline{\underline{\red{\sf{Answer :}}}}}$

Given :

A.P is => d + 2d + ...... + (n - 1)d

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Solution :

Here,

First Term (a) = d

last term (an or l) = (n -1)d

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We have formula for Sum of terms ,

$\Large{\underline{\boxed{\sf{S_{n} \: = \: \frac{n}{2} \: ( a \: + \: l)}}}}$

Put Values

⇒ Sn = n/2[d + (n - 1)d]

⇒ Sn = n/2 (d + nd - d)

⇒ Sn = n/2(nd)

⇒ Sn = n²d/2

$\Large{\boxed{\sf{S_{n} \: = \: \frac{n^2d}{2}}}}$

∴ Sum of n terms of an AP is n²d/2

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#answerwithquality

#BAL

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

According to the question given,

A.P → d + 2d + ...... + (n - 1)d

•First Term (a) = d

• last term (an or l) = (n -1)d

By using the formula for Sum of terms ,

$\tt\blue{S_{n} \: = \: \frac{n}{2} \: ( a \: + \: l)}$

By subsituting the values in given formula

⇒ Sn = n/2[d + (n - 1)d]

⇒ Sn = n/2 (d + nd - d)

⇒ Sn = n/2(nd)

⇒ Sn = n²d/2

$\tt\blue{S_{n} \: = \: \frac{n^2d}{2}}$

Hence the Sum of n terms of an AP is n²d/2