Question

find the sum of AP which contains 25 terms and whose term is 20​

Answer 1

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Answer 2

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$\textbf{Find the sum of 25 terms of an A.P} \\ \textbf{whose middle term is 20.}$

$\Large\bold\star\underline{\underline\textbf{Formula\:used}}$

• Middle term = ( First term + Last term )/2
• Sum of AP = n/2(First term + Last term)

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$\underline {\underline{\LARGE{{\bf{\green{S}}}{\mathfrak{o}}{\mathfrak{\orange{l}}}{\mathfrak{\red{u}}}{\mathfrak{\pink{t}}}{\mathfrak{\purple{i}}}{\mathfrak{\blue{o}}}{\mathfrak{\red{n}}}}}} : \:$

Let,

→ First Term of AP = a1

→ Last term = l (small L)

→ Number of terms = n

→ Middle term = m

so, we have

→ m = 20

→ n = 25 ...

From above told Middle term formula we get,

$20 = \frac{a_1 + l}{2} \\ \\ \red\longrightarrow \: (a_1 + l) = 40$

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Now putting this value in sum of n terms of AP with first term and last term , we get,

$S_n = \: \frac{n}{2} (a_1 + l) \\ \\ \green{putting \: values} \\ \\ \red\longrightarrow \: S_n \: = \frac{25}{2} \times (40) \\ \\ \red\longrightarrow \: S_n \: = \: 25 \times 20 \\ \\ \red\longrightarrow \: S_n \: = \: \bold{\boxed{\large{\boxed{\orange{\small{\boxed{\large{\red{\bold{\:500}}}}}}}}}} \:$

Hence, sum of 25 terms of AP is 500....

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$\large\underline\textbf{Hope it Helps You.}$

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