Three nonzero real numbers a,b,c are said to be in harmonic progression if `1/a + 1/c = 2/b.` Find the three- term harmonic progressions a,b,c of strictly increasing positive integers in which `a = 20 and b` divides c.

If 1 , a, b and 4 are in harmonic progression , then the value of a + b is equal to

Three numbers a, b and c are in geometric progression. If 4a, 5b and 4c are in arithmetic progression and a+b+c=70 , then the value of |c-a| is equal to

If a, b & 3c are in arithmetic progression and a, b & 4c are in geometric progression, then the possible value of (a)/(b) are

If three positive real numbers a, b, c are in AP with abc = 64, then minimum value of b is:

Let three positive numbers a, b c are in geometric progression, such that a, b+8 , c are in arithmetic progression and a, b+8, c+64 are in geometric progression. If the arithmetic mean of a, b, c is k, then (3)/(13)k is equal to

Let a,b,c , are non-zero real numbers such that (1)/(a),(1)/(b),(1)/(c ) are in arithmetic progression and a,b,-2c , are in geometric progression, then which of the following statements (s) is (are) must be true?

If a,b,c are in geometric progression and a,2b,3c are in arithmetic progression, then what is the common ratio r such that 0ltrlt1 ?

Let a_1,a_2,a_3,... be in harmonic progression with a_1=5a n da_(20)=25. The least positive integer n for which a_n<0 a. 22 b. 23 c. 24 d. 25

Let a, b, c and d are in a geometric progression such that a lt b lt c lt d, a + d=112 amd b+c=48 . If the geometric progression is continued with a as the first term, then the sum of the first six terms is

Three numbers a,b, and c form a Phythagorean triplet. If a=29, b=21, find c if c is the shortest of the three numbers.