Let $$S1$$,$$S2$$,$$S3$$… and $$t1$$,$$t2$$,$$t3$$… are two Arithmatic Sequence such that $$S1=t1$$≠$$0$$,$$S2=2t2$$ and ∑$$i=110$$ $$Si=$$∑$$i=115$$ ti then $$S2$$−$$S1t2$$−$$t1=d1d2$$ then $$d1$$−$$d2=$$

Question

Let $$S1$$,$$S2$$,$$S3$$… and $$t1$$,$$t2$$,$$t3$$… are two Arithmatic Sequence such that $$S1=t1$$≠$$0$$,$$S2=2t2$$ and ∑$$i=110$$ $$Si=$$∑$$i=115$$ ti then $$S2$$−$$S1t2$$−$$t1=d1d2$$ then $$d1$$−$$d2=$$

Infinity Learn · Accepted Answer

Given $$S1+S2+$$…$$+S10=t1+t2+$$…$$+t15$$ Let first sequence $$a1$$,$$a1+d1$$,$$a1+2d1$$,… and second sequence is $$a1$$,$$a1+d2$$,$$a2+2d2$$,… (sinc$$ $$s1=t1) Given $$S2=2t2a1+d1=2a1+d2a1=d1$$−$$2d2$$−−−$$1$$ We have to find ⇒$$S2$$−$$S1t2$$−$$t1=d1d2$$ Now $$1022a1+9d1=1522at1+14d2$$⇒$$a1=9d1$$−$$21d2$$−⋯−$$2$$ For $$1$$ and $$2$$⇒$$d1$$−$$2d2=9d1$$−$$21d28d1=19d2d1d2=198$$

$Let S_{1}, S_{2}, S_{3} \dots and t_{1}, t_{2}, t_{3} \dots are two Arithmatic Sequence such that$ $S_{1} = t_{1} \neq 0, S_{2} = 2 t_{2} and \sum_{i = 1}^{10} S_{i} = \sum_{i = 1}^{15} t_{i} then \frac{S_{2} - S_{1}}{t_{2} - t_{1}} = \frac{d_{1}}{d_{2}} then d_{1} - d_{2} =$

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Let S1,S2,S3… and t1,t2,t3… are two Arithmatic Sequence such that S1=t1≠0,S2=2t2 and ∑i=110 Si=∑i=115 ti then S2−S1t2−t1=d1d2 then d1−d2=

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$Let S_{1}, S_{2}, S_{3} \dots and t_{1}, t_{2}, t_{3} \dots are two Arithmatic Sequence such that$ $S_{1} = t_{1} \neq 0, S_{2} = 2 t_{2} and \sum_{i = 1}^{10} S_{i} = \sum_{i = 1}^{15} t_{i} then \frac{S_{2} - S_{1}}{t_{2} - t_{1}} = \frac{d_{1}}{d_{2}} then d_{1} - d_{2} =$