Question

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

`-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 term of the AP = `(-1)/2 + 1/6` 

= `(-2)/6`

= `(-1)/3`