the sum of n terms of an arithmetic sequence in 2nsquare-n .what is its nth term?
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Sn = 2n^2 - n
=> n/2 [ 2a + (n-1) d] = n ( 2n - 1)
=> 2a + (n-1) d = n (2n-1) × 2 / n
=> 2a + (n-1) d = 4n - 2
=> 2a +(n-1) d = 2 + 4n - 4
=> 2a + (n-1) d = 2 + 4 (n-1)
On comparing both sides, we get
2a = 2
=> a = 1
And,
d = 4
Now,
Tn = a + (n-1)d
= 1 + ( n-1) 4
= 1 + 4n - 4
= 4n - 3
=> n/2 [ 2a + (n-1) d] = n ( 2n - 1)
=> 2a + (n-1) d = n (2n-1) × 2 / n
=> 2a + (n-1) d = 4n - 2
=> 2a +(n-1) d = 2 + 4n - 4
=> 2a + (n-1) d = 2 + 4 (n-1)
On comparing both sides, we get
2a = 2
=> a = 1
And,
d = 4
Now,
Tn = a + (n-1)d
= 1 + ( n-1) 4
= 1 + 4n - 4
= 4n - 3
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