if the sum of n terms of an A.P. is n square +2x , find the A.P. and the 20th term.
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Sn = n² + 2n
we know,
Tn = Sn - Sn_1
= n² + 2n - (n -1)² -2(n -1)
= {n² - (n² -1)} + 2{ n - n +1 }
= 2n -1 +2
= 2n +1
so, Tn = 2n +1
then, A.P's are , 3 , 5 , 7, 9, 11 .......
20th term = 2(20) +1 = 41
we know,
Tn = Sn - Sn_1
= n² + 2n - (n -1)² -2(n -1)
= {n² - (n² -1)} + 2{ n - n +1 }
= 2n -1 +2
= 2n +1
so, Tn = 2n +1
then, A.P's are , 3 , 5 , 7, 9, 11 .......
20th term = 2(20) +1 = 41
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