Find four numbers forming a geometric progression in which the third t – InterviewSolution

InterviewSolution

1.	Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the `4^(t h)`by 18.
Answer» Let the required numbers be `a, ar, ar^(2)` and `ar^(3)`. Then, `T_(3)-T_(1)=9rArr ar^(2)-a=9rArr a(r^(2)-1)=9` ...(i) and `T_(2)-T_(4)=18 rArr ar-ar^(3)=18 rArr ar(1-r^(2))=18` ...(ii) On dividing (ii) by (i), we get `r=-2`. Putting `r=-2` in (i), we get `a(4-1)=9 rArr a=3`. Hence, the required numbers are 3, -6, 12 and -24.

Discussion

No Comment Found

Related InterviewSolutions

If `(a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0)`, then show that `a , b , c a n d d`are in G.P.
If p, q, r are in G.P. and the equations, `p x^2+2q x+r=0`and `dx^2+2e x+f=0`have a common root, then show that `d/p`,`e/q`,`f/r`are in A.P.
If `a a n d b`are the roots of `x^2-3x+p=0 a n d c , d`are the roots `x^2-12 x+q=0`where `a , b , c , d`form a G.P. Prove that `(q+p):(q-p)=17 : 15.`
If `a , b , c`are in A.P. `b , c , d`are in G.P. and `1/c ,1/d ,1/e`are in A.P. prove that `a , c , e`are in G.P.?
If `a ,b ,c`are in G.P. then prove that `(a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)`
If `S`be the sum, `P`the product and `R`the sum of the reciprocals of `n`terms of a G.P. prove that `(S/R)^n=P^2dot`
If `(a-b), (b-c),(c-a)`are in G.P. then prove that `(a+b+c)^2=3(a b+b c+c a)`
Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that `P^2R^n=S^n`.
Which of the foliowing statement(s) is/are true? (A) If `a^x =b^y=c^z and a,b,c` are in GP, then x, y, z are in HP (B) If `a^(1/x)=b^(1/y)=c^(1/z)` and `a,b,c` are in GP, then `x,y,z` are in AP
Find the sum of each of the following infinite series : `6+1.2+0.24+oo`