Let S1,S2,S3…………. and t1,t2,t3…………. are two arithmetic sequences such that S1=t1≠0;S2=2t2 and ∑i=110 Si=∑i=115 ti then, the value of S2−S1t2−t1 is:

Let S1,S2,S3…………. are in A.P. with common difference d and t1,t2,t3 are  in A.P with common difference d2. ∑i=110 Si=1022S1+(10−1)d1∑i=115 ti=1522t1+(15−1)d2102S1+9d1=152t1+14d222S1+9d1=32t1+14d22S1+9d1=3t1+7d22S1+9d1=3t1+21d2As, S1=t12t1+9d1=3t1+21d29d1=t1+21d2d1=S2−S1=2t2−t1d2=t2−t192t2−t1=t1+21t2−21t118t2−9t1=21t2−20t111t1=3t2 Thus, S2−S1t2−t1=2t2−t1t2−t1=2⋅113−1113−1=22−38=198