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Home » Justify whether it is true to say that –1, -3/2, –2, 5/2,… forms an AP as a2 – a1 = a3 – a2.
Justify whether it is true to say that –1, -3/2, –2, 5/2,… forms an AP as a2 – a1 = a3 – a2.
Arithmetic Progression | CBSE | Class 10 | Exercise 5.2 | Maths | NCERT Exemplar
Justify whether it is true to say that –1, -3/2, –2, 5/2,… forms an AP as a2 – a1 = a3 – a2.

Solution:

False

{{a}_{1}}~=\text{ }-1,\text{ }{{a}_{2}}~=\text{ }-3/2,\text{ }{{a}_{3}}~=\text{ }-2and {{a}_{4}}~=\text{ }5/2

{{a}_{2}}-{{a}_{1~}}=-3/2\left( -1 \right)\text{ }=-1/{{}_{2}}

{{a}_{3}}-{{a}_{2~}}=-2\left( -\text{ }3/2 \right)=-1/{{}_{2}}

{{a}_{4}}-{{a}_{3~}}=\text{ }5/2-\left( -2 \right)\text{ }=\text{ }9/2

We  can clearly say that, the difference of successive terms is not same, even though,{{a}_{2}}~-{{a}_{1}}~=\text{ }{{a}_{3}}-{{a}_{2}} but {{a}_{4}}-{{a}_{3}}~\ne \text{ }{{a}_{3}}-{{a}_{2}}~as a result it does not form an AP.

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