(i) The given progression 9, 15, 21, 27, ... .
Clearly, 15 − 9 = 21 − 15 = 27 − 21 = 6 (Constant)
Thus, each term differs from its preceding term by 6. So, the given progression is an AP.
First term = 9
Common difference = 6
Next term of the AP = 27 + 6 = 33
(ii) The given progression 11, 6, 1, −4, ... .
Clearly, 6 − 11 = 1 − 6 = −4 − 1 = −5 (Constant)
Thus, each term differs from its preceding term by −5. So, the given progression is an AP.
First term = 11
Common difference = −5
Next term of the AP = −4 + (−5) = −9
(iii) The given progression −1, , , , ...
Clearly, (Constant)
Thus, each term differs from its preceding term by . So, the given progression is an AP.
First term = −1
Common difference =
Next term of the AP =
(iv) The given progression
This sequence can be re-written as
Clearly, (Constant)
Thus, each term differs from its preceding term by . So, the given progression is an AP.
First term =
Common difference =
Next term of the AP =
(v) The given progression
This sequence can be re-written as
Clearly, (Constant)
Thus, each term differs from its preceding term by . So, the given progression is an AP.
First term =
Common difference =
Next term of the AP =