if sn the sum of first n terms of an a.p is given by sn=5n^2+3n then find its nth term ??
(please explain you procedure)

 

dear student,
 
according to the question, the sum of first n term of the ap is given by,
 
sn = 5n2 + 3n
 
now, the sum of first (n-1) terms will be given by
 
sn-1 = 5(n-1)2 + 3(n-1)
 
=> sn-1 = 5n2 + 5 - 10n + 3n - 3 = 5n2 - 7n + 2
 
now, the difference between sn and sn-1 is equal to the nth term,
 
sn - sn-1 = 5n2 + 3n - 5n2 + 7n - 2
 
=> tn = 10n - 2
 
 
regards topperlearning.