# 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, if are 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 