Sequences and Series
The least length of the thread required to construct a rectangle of area 256 cm2 is
area =ab256=ab2(a+b)=p2(a+a256)=puse AM & GM2a+a256≥(a×a256)21a+a256≥32p≥64
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Show that a1,a2,…,an,…form an AP where anis defined as below : (i) an=3+4n (ii) an=9−5n. Also find the sum of the first 15 terms in each case.
What is the 20thterm of the sequence defined by an=(n−1)(2−n)(3+n)?
How many two–digit numbers are divisible by 3?
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A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 0 paise to mail one letter. Find the amount spend on the postage when 8th set of letter is mailed.
The difference between any two consecutive interior angles of a polygon is 5o. If the smallest angle is 120o, find the number of the sides of the polygon.
Find the sum of first 24 terms of the list of numbers whose nth term is given by an=3+2n