Page 26 - Mathematics Class - X

Fig. (a) Fig. (b)

OBSERVATIONS
Fig. (a) Fig. (b)

The difference of heights of first two strips is equal to The difference of heights of first two strips is
1 unit. equal to 3 units.

The difference of heights of second and third strips is The difference of heights of second and third
equal to 3 units. strips is equal to 3 units.

The difference of heights of third and fourth strips is The difference of heights of third and fourth
equal to 4 units. strips is equal to 3 units.
Difference is not uniform. Difference is uniform.

So, the list of numbers 1, 2, 5, 9, ... does not form an AP. So, the list of numbers 2, 5, 8, 11, ... form an AP.

INFERENCE
It is clear that difference of heights of two consecutive strips is same throughout in Fig. (b), so sequence (ii),
i.e., 2, 5, 8, 11, ............ is an AP.

EXTENDED TASK
1. To find experimentally, whether the given sequence of numbers is an arithmetic sequence (progression) or not.

(i) 3, 8, 13, 18, ... (ii) 4, 7, 11, 16, ... (iii) 7, 10, 13, 16,...
2. Check whether the series 5, 8, 11, 14, 17 is an arithmetic sequence or not.

APPLICATION
This activity helps in finding whether the given sequence is an arithmetic sequence or not.

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