# The numbers  and  are between 2 and 18, such that 1. Their sum is 25 2. The numbers  and  are consecutive terms of an A.P. 3. The numbers  are consecutive terms of a G.P. The value of  is a) 500 b) 450 c) 720 d) None of these

## Question ID - 51132 :- The numbers  and  are between 2 and 18, such that 1. Their sum is 25 2. The numbers  and  are consecutive terms of an A.P. 3. The numbers  are consecutive terms of a G.P. The value of  is a) 500 b) 450 c) 720 d) None of these

3537

(d)

We have,

(1)

(2)

(3)

Eliminating  from (1) and (2), we have

Then from (3),

Now,  is not possible since it does not lie between 2 and 18. Hence, . Then from (3),  and finally from (2),

Thus,  and . Hence,

Also, equation  is , which has imaginary roots

If  are roots of the equation , then sum of product of roots taken two at a time is

Next Question :
 Let  be the terms of a sequence and let Case I: If  are in A.P., then  is quadratic in ‘’. If  are in A.P., then  is cubic in Case II: If  are not in A.P., but in G.P., then , where  is the common ratio of the G.P.  and  Again, ifare not in G.P. but  are in G.P., then  is of form  and  is the common ratio of the G.P.  and The sum of 20 terms of the series  is a) 4010 b) 3860 c) 4240 d) None of these