State if the following is true or false.

In the following situation, the list of numbers involved arithmetic progression.

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

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True

False

answer is A.

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Detailed Solution

Given that,
The length of rungs of a ladder when the bottom rung is 45 cm and length of rungs decreases by 2 cm from top to bottom.
Now,
The length of the 2nd rung is

45 − 2 = 43

.
The length of the 3rd rung is

43 − 2 = 41

.
Therefore, lengths(in cm’s) of the 1st, 2nd, 3rd rungs from bottom to top respectively are 45,43,41,....
Now, the common difference is,

\Rightarrow a_{2} - a_{1} = 43 - 45

\Rightarrow a_{2} - a_{1} = - 2

And,

\Rightarrow a_{3} - a_{2} = 41 - 43

\Rightarrow a_{3} - a_{2} = - 2

Difference between the 3rd and 2nd term is equal to the difference between the 2nd and 1st term.
Hence, the length of the rungs forms an AP.
The length of the rungs forms an AP.
Therefore, the statement is true.
Hence, option 1 is correct.

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