ahmed786

Please solve these
1)
Insert n A.Ms between 1 and n²

2)
b+c-3a/a , c+a-3b/b , a+b-c/c are in A.P prove that 1/a , 1/b , 1/c are also in A.P

3)
If the roots of equation a(b-c)x² + b(c-a)x + c(a-b) = 0 are equal, prove that a, b, c are in H.P.

4)
The sums of the first n terms of two A.P.s are in the ratio 3n+31 : 5n-3 find the ratio of their nth terms.

5)
If G1 and G2 are two G.M.s between b,c and A is their A.M., then show that G1^3 + G2^3 = 2Abc

6)
If a,b,c in G.P. and x,y are the A.M.s of a, b and b, c respectively, then prove that a/x + c/y = 2

7)
An A.P. has first term of 6 and fifth term of 18 find the sum of the n terms of the progression is greater than 2000

8)
Find a G.M. between 3 and 12

9)
Sum to n terms the series 2+22+222....

skipjack

(6). Using b = ar and c = ar², show that 2a/(a + ar) + 2ar²/(ar + ar²) = 2, which is easy to do.

(7). n needs to be at least 27.

(8). 6

(9). (2/81)(10^(n+1) - 9n - 10)