The sum of the first n terms of an AP is 5n-n2 . Find the nth term of is AP.
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Answered by
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Sn = 5n - n²
° S1 = 5 × 1 - ( 1 )²
S1 = 5 - 1
S1 = 4
• a1 = S1
a1 = 4
° S2 = 5 × 2 - ( 2 )²
S2 = 10 - 4
S2 = 6
• a2 = S2 - S1
a2 = 6 - 4
a2 = 2
d ( common difference ) = a2 - a1
d = 2 - 4 = - 2
To find nth term ,
an = a + ( n - 1 )d
an = 4 + ( n - 1 ) ( - 2 )
an = 4 - 2n + 2
an = 6 - 2n
° S1 = 5 × 1 - ( 1 )²
S1 = 5 - 1
S1 = 4
• a1 = S1
a1 = 4
° S2 = 5 × 2 - ( 2 )²
S2 = 10 - 4
S2 = 6
• a2 = S2 - S1
a2 = 6 - 4
a2 = 2
d ( common difference ) = a2 - a1
d = 2 - 4 = - 2
To find nth term ,
an = a + ( n - 1 )d
an = 4 + ( n - 1 ) ( - 2 )
an = 4 - 2n + 2
an = 6 - 2n
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