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:

Question

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:

Infinity Learn · Accepted Answer

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, $$S2$$−$$S1t2$$−$$t1=2t2$$−$$t1t2$$−$$t1=2$$⋅$$113$$−$$1113$$−$$1=22$$−$$38=198$$

$Let S_{1}, S_{2}, S_{3} \dots \dots \dots \dots . and t_{1}, t_{2}, t_{3} \dots \dots \dots \dots . are two arithmetic sequences such that$ $S_{1} = t_{1} \neq 0; S_{2} = 2 t_{2} and \sum_{i = 1}^{10} S_{i} = \sum_{i = 1}^{15} t_{i} then, the value of \frac{S_{2} - S_{1}}{t_{2} - t_{1}} is:$

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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:

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$Let S_{1}, S_{2}, S_{3} \dots \dots \dots \dots . and t_{1}, t_{2}, t_{3} \dots \dots \dots \dots . are two arithmetic sequences such that$ $S_{1} = t_{1} \neq 0; S_{2} = 2 t_{2} and \sum_{i = 1}^{10} S_{i} = \sum_{i = 1}^{15} t_{i} then, the value of \frac{S_{2} - S_{1}}{t_{2} - t_{1}} is:$