In which of the following situation, the sequence of numbers formed will form an A.P.?

(i) The cost of digging a well for the first metre is Rs. 150 and rises by Rs.20 for each succeeding metre.

(ii)The mount of air present in the cylinder when a vacuum pump removes each time of their remaining in the cylinder.

(i) The cost of digging a well for the first metre = Rs. 150

The cost of digging a well for the second metre = 150 + 20 = Rs. 170

The cost of digging a well for the third metre = 170 + 20 = Rs. 190

The cost of digging a well for the fourth metre = 190 + 20 = Rs. 210

Difference between first and second metre = 170 – 150 = 20

Difference between second and third metre = 190 – 170 = 20

Difference between third and fourth metre = 210 – 190 = 20

Since, all the differences are equal. Therefore, it’s an A.P.

(ii) Let the amount of air present in the cylinder first time = x

Amount of air present in the cylinder second time = x - =

Amount of air present in the cylinder third time = - =

Difference in the amount of air present in the cylinder between first and the second time = – x =

Difference in the amount of air present in the cylinder between second and the third time = -

=

Since, the differences are unequal. Therefore, it’s not an A.P.