Sequences and Series
The sum of the 4th and 8th term of an A.P is 24 and the some of its 6th and 10th terms is 44. Find the first terms ?
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If a,b and c are positive and 9a+3b+c=90 then the maximum value of (loga+logb+logc ) is (Base of the logarithm is 10)
If m arithmetic means are inserted between 1 and 31 so that the ratio of the 7th and (m−1)th means is 5:9, then the value of m is
Let A1 denotes arithmetic mean of two numbers a=1b=2. A2 denotes arithmetic mean of A1 and b. For n≥3,let An is arithmetic mean of An−1 and b , then
If G is the geometric mean of x and y, then tG2−x21+G2−y21=G21
If a,b,c are three positive numbers,then the minimum value of the expression bcaab(a+b)+bc(b+c)+ca(c+a)
If x2+y2+z2=1 then the value of xy+yz+zx lies in the interval
Find three arithmetic means between 6 and −6.
For any two positive numbers,we have