Question

If the sum of nth terms of an A.P.is 2n+3n² .find the nth term​

Answer 1

Question:-

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If the sum of nth terms of an A.P is 2n + 3n². Find the nth term

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Given:-

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• Sum of the nth terms of an A.P is 2n + 3n².

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To Find :-

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• The nth term.

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Solution :-

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$\pmb {s_{1} = 2(1) + 3(1)^{2} = 5}$

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$\pmb { s_{n} = \frac{n}{2} \{2a + (n - 1)d \}}$

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$\pmb { s_{n} = \frac{n}{2} \{a + a + (n - 1)d \}}$

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$\pmb{ s_{n} = \frac{n}{2} \{a + a_{n} \} }$

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$\pmb{2n + 3n^{2} = \frac{n}{2} \{5 + a_{n} \} }$

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$\pmb{ 4 + 6n = 5 + a_{n} }$

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$\pmb{ a_{n} = 6n - 1 }$

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