## Question

#### SIMILAR QUESTIONS

Let n ∈ **N, **n > 25. Let *A, G, H *denote the arithmetic mean, geometric mean and harmonic mean of 25 and n. The least value of n for which *A, G, H *∈ {25, 26, …, n}, is

Let a, b, c be distinct real numbers which are in G.P. If ∈ **R **is such that a + *x, *b* + x, *c + *x, *are in H.P., then *x *equals * *

Let a, b, c be in A.P., and (b – c) x^{2 }+ (c – a) x +(a – b) = 0 and 2(a + c) x^{2} +(b + c) x = 0 have a common root, then

Suppose a, b, c are in A.P. Let A, G bet the arithmetic mean and geometric mean between a and b, A’ , G’ bet the arithmetic mean and geometric mean between b and c, then

In a sequence of 21 terms the first 11 terms are in A.P. with common difference 2 and the last 11 terms are in G.P. with common ratio 2. If the middle terms of the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is