11. The sum of the 5th and 24th terms of an arithmetic sequence is 50. Find the sum of the Ist and 28th terms?
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the criteria for choosing the method for separating the components of a mixture are Chromatography, separating funnel, evaporation, distillation, fractional distillation etc
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Solution :-
The two series are in A.P. Therefore, the common series will also be in an A.P
Common difference of 1st series =4 and the common difference of 2nd series =5.
Common difference of the sequence whose terms are common to the two series is given by L.C.M of 4 and 5 =20
Here the first term of the identical (common terms) sequence is 19.
We know the sum of first n terms is given by = 2n[2a+(n+1)d]
Hence,
the sum of first 50 terms of this sequence = 250[2×19+(50+1)20]=25450
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