1.   In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?

(i)  The taxi fare after each km when the fare is ₹ 15 for the first km and ₹ 8 for each additional km.

(ii)  The amount of air present in a cylinder when a vacuum pump removes $1/4$ of the  air remaining in the cylinder 
     at a time.

(iii)  The cost of digging a well after every metre of digging, when it costs ₹ 150 for the first metre and rises
     by ₹ 50 for each subsequent metre.
	 
(iv)  The amount of money in the account every year, when ₹ 10000 is deposited at compound interest at 8 % per annum.

2.   Write first four terms of the AP, when the first term a and the common difference d are given as follows:
(i)  a = 10,        d = 10                               (ii)  a = –2,    d = 0
(iii)  a = 4,       d = – 3                             (iv)  a = – 1,   d = $1/2$
(v)  a = – 1.25,  d = – 0.25

3. For the following APs, write the first term and the common difference:
 (i)  3, 1, – 1, – 3, . . .                                       
(ii)  – 5, – 1, 3, 7, . . .
(iii)$1/3,5/3,9/3,13/3$
(iv)  0.6, 1.7, 2.8, 3.9, . . . 

4.   Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
(i)   2, 4, 8, 16, . . .                          (ii)  2,$5/2$,3,$7/2$
(iii)   – 1.2, – 3.2, – 5.2, – 7.2, . . .        (iv)  – 10, – 6, – 2, 2, . . .
(v)   3, 3 +√2, , 3 + 2√2,, 3 + 3√2,  . . .     (vi)  0.2, 0.22, 0.222, 0.2222, . . . 
(vii)   0, – 4, – 8, –12, . . .                  (viii) $-1/2,-1/2,-1/2$,.....
(ix)  1, 3, 9, 27, . . .                        (x)  $a, 2a, 3a, 4a, . . . $
(xi)   $a, a^2, a^3, a^4, . . .$               (xii) √2,√8,√18,√32
(xiii) √3,√6,√9,√12                            (xiv)  $ 1^2, 3^2, 5^2, 7^2, . . .$