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State if the following is true or false.

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

The money saved by Sudha in successive years when she saves Rs. 100 the first year and increased the amount by Rs. 50 every year.

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True

False

answer is A.

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Detailed Solution

According to the question,
The money saved by Sudha in successive years when she saves rupees 100 the first year and increased the amount by rupees every year
Now, the amount saved in the second year after Sudha will be,

\Rightarrow a_{2} = 100 + 50

\Rightarrow a_{2} =

150
Similarly, the amount saved in the third year after Sudha will be,

\Rightarrow a_{3} = 150 + 50

\Rightarrow a_{3} = 200

Therefore, the series is 100,150,200,....
Now, the common difference will be,

\Rightarrow a_{2} - a_{1} = 150 - 100

\Rightarrow a_{2} - a_{1} = 50

Also,

\Rightarrow a_{3} - a_{2} = 200 - 150

\Rightarrow a_{3} - a_{2} = 50

The difference between the

3^{rd}

and the

2^{nd}

term is equal to the difference between the

2^{nd}

and

1^{st}

term.
Hence, it forms an AP
The list of numbers forms an arithmetic progression with

a = 100, d = 50

, since the difference between each term of the sequence is 50
Therefore, the statement is true.
Hence, option 1 is correct.

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