In which of 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.
Given:
The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 20 for each succeeding metre.
To do:
We have to check whether the sequence formed by the above information is an A.P.
Solution:
The cost of digging the well for the first metre$= Rs.\ 150$.
The cost of digging the well for the second metre$= Rs.\ (150+20)=Rs.\ 170$.
The cost of digging the well for the third metre$= Rs.\ (170+20)=Rs.\ 190$.
The cost of digging the well for the fourth metre$= Rs.\ (190+20)=Rs.\ 210$.
The cost of digging the well for each successive metre (in rupees) forms the below sequence
$150, 170, 190, 210, ........$
Here, $a=150$ and $d=170-150=20$.
Therefore, the sequence of the numbers formed is an A.P.
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