Question

the sum of first n term of an ap is 5n square - 3n find nth term and also 10th term

Answer 1

given ,
Sn=5n^2-3n

but we know sum of nth term formula is ----
Sn=n/2 {2a+(n-1) d}
so, we convert given Sn into formula ,

Sn=5n^2-3n
=n {5n-3}
=n/2{10n-6}
Sn=n/2 {2.2+(n-1)10} -------(1)

now equation (1) is in formula type
where a=2 and d =10
now,
tn=a+(n-1) d =2+(n-1) 10=10n-8

t10= 10 x 10-8 = 92

Answer 2

given sn = 5n²-3n

s1 = 5*1²-3*1 =5-3 =2
s2= 5*2²-3*2 =20-6 =14

s3 = 5*3²-3*3 =45-9=36
a1=s1=2

a2= s2-s1 = 14-2 =12
a3= s3-s2=36-14 =22

first term = a =a1 = 2
common difference = d= a2-a1 =12-2 =10

nth term in ap=an = a+(n-1)d
a10 = 2 +(10-1)10
=2+9*10
=2+90
=92