Let
Sn=3+7+14+24+37+.....Tn
Sn= 3 + 7+14+24+......Tn-1+Tn
Subtracting
0=3+(4+7+10+.......(n-1)the term-Tn
Tn=3+(n-1)/2[2×4+(n-2)×3]
Tn=(n-1)/2(3n+2)+3
Tn=1/2(3n^2-n-2)+3
Tn=3/2n^2-1/2n+2
Putting n= 1 to 10 and summing
S10 =3/2(1^2+2^2+3^2+...+10^2)-1/2(1+2+3+4+....+10)+2×10
=3/12×(10×11×(2×10+1)-1/4(10×11)+20
=1/4×110×21-110/4+20
=1/4×20×110+20
=5×110+20
=550+20
=570
So option should be (b)
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