Question

if Sn =n^2-3 find 7th term of A P​

Answer 1

Step-by-step explanation:

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Answer 2

$Given \: sum \:of \: n \:terms (S_{n}) = n^{2}-3$

$Now, n^{th} \:term\: in \: A.P \: (a_{n})$

$= S_{n} - S_{n-1}$

$= n^{2} - 3 - [(n-1)^{2} - 3]$

$= n^{2} - 3 - ( n^{2} - 2n + 1^{2} - 3 )$

$= n^{2} - 3 - n^{2} + 2n - 1 + 3$

$= 2n - 1$

$\therefore a_{n} = 2n-1$

$If \: n = 7 \:then \: a_{7} = 2\times 7 - 1$

$\implies a_{7} = 14 - 1$

$\implies a_{7} = 13$

$\red { 7^{th} \:term \: of \:A.P } \green { = 13 }$

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