The sum of first n term of A.P. is 5n square - 3n. Find the A.P. and hence find its 12th term.
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given:Sn=5n^2-3n
to find :the A.P and its 12th term
S1=5(1)^2-3(1)=2
S1=Sum of first term=first no. of the A.P.
so a1=2
S2=5(2)^2-3(2)
=14
S2=a1+a2
so a2=S2-a1
=14-2
=12
d=a2-a1
so d=12-2
=10
so a3=a2+10=12+10=22
and a4=a3+10=22+10=32
so A.P. is 2,12,22,32....
an=a+(n-1)d
so a12=2+(12-1)10
=2+(11*10)
=2+110
=112
so A.P. is 2,12,22,32...
and a12=112
to find :the A.P and its 12th term
S1=5(1)^2-3(1)=2
S1=Sum of first term=first no. of the A.P.
so a1=2
S2=5(2)^2-3(2)
=14
S2=a1+a2
so a2=S2-a1
=14-2
=12
d=a2-a1
so d=12-2
=10
so a3=a2+10=12+10=22
and a4=a3+10=22+10=32
so A.P. is 2,12,22,32....
an=a+(n-1)d
so a12=2+(12-1)10
=2+(11*10)
=2+110
=112
so A.P. is 2,12,22,32...
and a12=112
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