Question

The hand- borewell driller charges Rs. 200 for the first one metre only and raises drilling charges at the rate of Rs. 30 for every subsequent metre. Write a progression for the above data.

Answer 1

Hint: Here, we can observe that the drilling charges are always raised at the rate of Rs. 30 for every subsequent metre after the first metre that is a constant. So, this sequence will form an AP.

Complete step-by-step answer:
Since, we know that the difference between any two consecutive terms of an AP is always constant and this constant is the common difference of the AP.
So, when we look at the case given in this question, we come to know that:
Charge of hand-borewell digger for first 1 metre = Rs. 200
Rate of increase of charge after the first 1 metre is = Rs.30 per metre
So, charge for 2 metres will be = Rs. 200 + Rs. 30
                                                        = Rs. 230
Similarly, for 3 metres charge will be = Rs. 230 + Rs. 30
                                                                   = Rs. 260
So, the sequence formed is:
200, 230, 260,…….
So, here the difference between two consecutive terms is always constant.
So, this sequence is an AP with first term = 200 and the common difference of this AP is 30.
Hence, the progression 200, 230, 260, …… so obtained is an arithmetic progression.

Note: Students should note here that in AP only the difference of the consecutive terms is always constant and the common difference of an AP is given as a term subtracted from its successive term.