Q7 of 176 Page 9

In which of the following situations does the list of numbers involved arithmetic progression, and why?

The lengths of the rungs of a ladder when the bottom rung is 45cm, and length of rungs decrease by 2 cm from bottom to top.


The length of the bottom rung = 45cm


According to the question,


Length of rungs decreases by 2cm from bottom to top. The lengths (in cm) of the 1st, 2nd, 3rd, … from the bottom to top respectively are 45, 43, 41, …


Difference between 2nd and 1st term = 43 – 45 = -2


Difference between 3rd and 2nd term = 41 – 43 = -2


Since, the difference is same.


Hence, the length of the rungs form an AP with a = 45cm and d = -2 cm.


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