This is the basic and conceptual question from arithmetic progression chapter and it was already asked in previous year paper of 2011 in which we have to find the difference between the sums of the first 50 terms if two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively.
RS Aggarwal, Class 10, chapter 5C, question no 30
For first A.P
S1n=(n/2)(2n+(n−1)d)
S130=(30/2)(2×3+(30−1)d)
S130=15(6+29d)
S130=90+435d
For second AP
S2n=(n/2)(2n+(n−1)d)
S230=(30/2)(2×8+(30−1)d)
S230=15(16+29d)
S230=240+435d
Difference between S130−S230=(90+435d)−(240+435d)=150