The sum of first m terms of an A.P. is 4m² − m. If its nth term is 107. find the value of n. Also, find the 21st term of this A.P.

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Solution

$S_{m} = 4 m^{2} - m We know a_{m} = S_{m} - S_{m - 1} ∴ a_{m} = 4 m^{2} - m - 4 {(m - 1)}^{2} + (m - 1) a_{m} = 8 m - 5 Now, a_{n} = 107 \Rightarrow 8 n - 5 = 107 \Rightarrow 8 n = 112 \Rightarrow n = 14 a_{21} = 8 (21) - 5 = 163$

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The sum of first m terms of an A.P. is $4 m^{2}$ -m. If its nth terms is 107, find the value of n. Also, find the 21st term of this A.P.

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The sum of first m terms of an AP is $(4 m^{2} - m)$ . If its nth term is 107, find the value of n. Also, find the 21st term of this AP.

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