1.)If 1/2,1/x,1/3 are successive terms of an A.P shows that

2-x/x-3=2/3
2.)write down a recurrence relation between the terms of the sequence 5,14,41,122,...

1 answer

it's an AP, so
1/x - 1/2 = 1/3 - 1/x
(2-x)/2x = (x-3)/3x
and so on

Look at the differences
5 14 41 122
. 9 27 81
those are powers of 3, so ...