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The taxi fare after each km, when the fa...

The taxi fare after each km, when the fare is Rs. 15 for the first km and Rs 8 for each additional km, does not form an AP as the total fare (in Rs.) after each km . Is the statement true? Give reasons.

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No, because the total fare (in Rs.) after each km is
` " " 15,(15+8),(15+2xx8),(15+3xx8),…=15,23,31,39,…`
Let `t_(1)=15,t_(2)=23,t_(3)=31` and `t_(4)=39`
Now, `t_(2)-t_(1)=23-15=8`
` " " t_(3)-t_(2)=31-23=8`
` " " t_(4)-t_(3)=39-31=8`
Since, all the successive terms of the given list have same difference i.e., common defference `=8`
Hence, the total fare after each km form an AP.
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The taxi fare after each km when the fare is Rs 15 for the first km and Rs8 for each additional km

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NCERT EXEMPLAR-ARITHMETIC PROGRESSIONS-Arithmetic Progressions
  1. Two A.P have the same common difference. The first term of one A.P is ...

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  2. Is 0 a term of the AP 31, 28, 25, …? Justify your answer.

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  3. The taxi fare after each km, when the fare is Rs. 15 for the first km ...

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  4. In which of the following situations, do the lists of numbers involved...

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  5. Justify whether it is true to say that the following are the nth terms...

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  6. Match the AP's given in column A with suitable common differences giv...

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  7. Verify that each of the following is an AP and then write its next thr...

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  8. Write the first three terms of the AP's, when a and d are as given bel...

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  9. Find a, b and c such that the following numbers are in AP, a, 7, b, 23...

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  10. Determine the AP whose fifth term is 19 and the difference of the eigh...

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  11. The 26th, 11th and the last terms of an AP are, 0, 3 and -(1)/(5), res...

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  12. The sum of the 5th and the 7th terms of an AP is 52 and the 10th term ...

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  13. Find the 20th term of the AP whose 7th term is 24 less than the 11th t...

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  14. If the 9th term of an AP is zero, then prove that its 29th term is twi...

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  15. Find whether 55 is a term of the AP 7, 10, 13, … or not. If yes, find ...

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  16. Determine k, so that K^(2)+4k+8, 2k^(2)+3k+6 and 3k^(2)+4k+4 are three...

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  17. Split 207 into three parts such that these are in AP and the product o...

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  18. The angles of a triangle are in A.P. The greatest angle is twice the l...

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  19. If the nth terms of the two AP's 9, 7, 5, … and 24, 21, 18, … are the ...

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  20. If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7...

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