Question

Show that each of the progressions given below is an AP. Find the first term, common  difference and next term of each .

(iii)-1 `, (-5)/6 , (-2)/3 , (-1)/2 ............` 

Answer 1

The given progression -1 `, (-5)/6 , (-2)/3 , (-1)/2 ............` 
Clearly,  ` (-5)/6 - (-1) = (-2)/3 - ((-5)/6) = (-1)/2- ((-2)/3 ) = 1/6 `(Constant)
Thus, each term differs from its preceding term by`1/6` So, the given progression is an
AP.
First term = –1
Common difference =`1/6`
Next tern of the  AP = `(-1)/2 + 1/6 = (-2)/6 = (-1)/3`