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प्रश्न
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.
उत्तर
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
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संबंधित प्रश्न
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Two A.P.’s have the same common difference. The first term of one A.P. is 2 and that of the other is 7. Show that the difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms.
Common difference, d = ? for the given A.P., 7, 14, 21, 28 ........
Activity :- Here t1 = 7, t2 = 14, t3 = 21, t4 = `square`
t2 − t1 = `square`
t3 – t2 = 7
t4 – t3 = `square`
Therefore, common difference d = `square`
