Math, asked by archanamondal630, 2 days ago

verify that common difference is same in an arithmetic progression by activity method

Answers

Answered by sheebakhan8103

A sequence of numbers in which every term except the first term is obtained by adding a fixed number to its preceding term is called an arithmetic progression (AP).

Procedure

Step 1: Mark both the sheets of graph paper with squares (each side = 1 unit).

Step 2: Mark x- and y-axes on each sheet of graph paper.

Step 3: We shall first test if the sequence 2,5,8,11,14,… is an AP.

Step 4: Cut the paper tape in rectangular strips of lengths 2 units, 5 units, 8 units, 11 units, 14 units,….

Step 5: Using the x-axis as the base, paste the strips on graph paper I sequentially (as shown in Figure 2.1). Record your observations in the first observation table.

Math Labs with Activity – Sequence of Numbers is an Arithmetic Progression (AP) 1

Step 6: We shall now test if the sequence 2,6,9,13,16,… is an AP.

Step 7: Cut the paper tape in rectangular strips of lengths 2 units, 6 units, 9 units, 13 units, 16 units,….

Math Labs with Activity – Sequence of Numbers is an Arithmetic Progression (AP) 2

Step 8: Using the x-axis as the base, paste the strips on graph paper II sequentially (as shown in Figure 2.2). Record your observations in the second observation table.

Observations

I. For Figure 2.1

Math Labs with Activity – Sequence of Numbers is an Arithmetic Progression (AP) 3

Math Labs with Activity – Sequence of Numbers is an Arithmetic Progression (AP) 4

Conclusions

The sequence 2, 5, 8, 11, 14, … forms a uniform ladder having equal steps (as shown in Figure 2.1) and has a common difference d = 3 units (see the first observation table). Hence, this sequence is an AP.

The sequence 2,6,9,13,16,… forms a ladder but of unequal steps (as shown in Figure 2.2) and the common difference (d) does not exist (see the second observation table). Hence, this sequence is not an AP.

Math Labs with ActivityMath LabsScience Practical SkillsScience Labs

Filed Under: CBSE

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