Question

Given a sequence of 4 numbers, first three of which are in A.P. and the last three in G.P. with common ratio $\frac{3}{2}$.If 1 is subtracted from the last number, all the four numbers in order form an A.P., then the value of sum of smallest and largest of the four numbers is

• A. 10
• B. 13
• C. 12
• D. 11

Answer 1

Answer: (D)

4 numbers:
$a - d , a , a + d , a +2 d +1 $
$\frac{3}{2} a =( a + d ), $
$ ( a +2 d +1)=( a + d ) \cdot \frac{3}{2} $
$3 a =2 a +2 d $
$ 2 a +4 d +2=3 a +3 d $
$a =2 d \ldots . . .( i ) $
$ a - d =2$ .....(ii)
From (i) and (ii),
$a=4, d=2$
$\therefore $ smallest number $=2$, largest number $=9$