Question

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

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

Answer 1

In the given problem,

Cost of digging a well for the first meter = Rs 150

Cost of digging a well for the subsequent meter is increased by Rs 20

So,

Cost of digging a well of depth one meter= Rs. 150

Cost of digging a well of depth two meters= Rs 150 + 20 = Rs 170

Cost of digging a well of depth three meters= Rs 150 + 20 + 20 = Rs 190

Cost of digging a well of depth four meters = Rs 150 + 20 + 20 + 20 = Rs 210

Thus, the costs of digging a well of different depths are  150, 170, 190, 210,...

Now, for a sequence to be an A.P., the difference between adjacent terms should be equal.

Here

`a_1 - a = 170 - 150`

= 20

Also

`a_2 - a_1 = 190 - 170`

= 20

Therefore `a_1 - a = a_2 - a_1`

Since the terms of the sequence are at a common difference of 20, the above sequence is an A.P. with the first term as a = 150 and common difference d = 20