If p is the first of the n arithmetic means between two numbers and q be the first on n harmonic means between the same numbers. Then, show that q does not lie between p and ((n+1)/(n-1))^2 p.
If H_(1) , H_(2) are two harmonic means between two positive numbers a and b , (a != b) , A and G are the arithmetic and geometric means between a and b , then (H_(2) + H_(1))/(H_(2) H_(1)) is
The difference between the sum of squares of first n natural numbers and the sum of first n natural numbers is always divisible by 2.
If nine arithmetic means and nine harmonic means are inserted between 2 and 3 alternatively, then prove that A+6//H=5 (where A is any of the A.M.'s and H the corresponding H.M.) dot
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A. P. and the ratio of 7^(th) and (m - 1)^(th) numbers is 5 : 9. Find the value of m.
The mean of 12 numbers is 20, if each number is multiplied by 6, then the new mean is …………….. .
There are four unknown numbers. The mean of the first two numbers is 4 and the mean of the first three is 9. The mean of all four number is 15, if one of the four number is 2 find the other numbers.
Find three numbers a,b,c between 2 & 18 such that; (G) their sum is 25 (ii) the numbers 2,a,b are consecutive terms of an AP & (ii) the numbers b,c, 18 are consecutive terms of a G.P.
CENGAGE-PROGRESSION AND SERIES-ARCHIVES (MATRIX MATCH TYPE )
