Question

In an AP if Sn =4n-n2 then ""a2 = —————""​

Answer 1

$Given \: sum \:of \: n \:terms \: S_{n} = 4n - n^{2}$

$n^{th} \:term \:(a_{n}) = S_{n} - S_{n-1}$

$Here , n = 2$

$2^{nd} \:term \:(a_{2}) \\= S_{2} - S_{2-1} \\= \\S_{2} - S_{1} = (4 \times 2 - 2^{2} )- ( 4\times 1 - 1^{2} )\\= 8 - 4 - ( 4 - 1 ) \\= 4 - 3 = 1$

Therefore .,

$\red{2^{nd} \:term \:(a_{2})} \green { = 1 }$

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Answer 2

Given : Sₙ=4n-n²,

To Find :   the value of a₂

Solution:

a₂  = S₂ - S₁

=> a₂   = 4*2 -2² -   (4*1 -1² )

=> a₂   =8 -4  -   (4 -1 )

=> a₂   = 4  -   (3 )

=>  a₂   =  1

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