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Mathematics Lab Activity-08 Class X | Arithmatic Progression
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Mathematics Lab Activity-08 Class X
Chapter - 05
arithmatic progression
Activity - 08
Objective1. Take a rectangular cardboard of a convenient size and paste a white paper on it. Draw a rectangle ABCD of length (2a+9d) units and breadth 10 units.
2. Make some rectangular strips of equal length a units and breadth one unit and some strips of length d units and breadth 1 unit, using coloured drawing sheets.
3. Arrange/paste these strips on the rectangle ABCD as shown in Fig. 1.
4. The
strips so arranged look like a stair case.
5. The
first stair is of length a units, the second stair is of length a + d (units),
third of a + 2d units and so on and each is of breadth 1 unit. So, the areas
(in sq. units) of these strips are a, a + d, a + 2d, ....., a + 9d,
respectively
6. This
arrangement of strips gives a pattern a, a + d, a + 2d, a + 3d, ...
which is an
AP with first term a and the common difference d.
Observations & calculations
1. The sum
of the areas (in square units) of these strips
= a + (a +
d) + (a + 2d) + ... + (a + 9d) = 10a + 45d ....... (1)
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