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Home » 2. Show that the sequence defined by an = 3n2 – 5 is not an A.P.
2. Show that the sequence defined by an = 3n2 – 5 is not an A.P.
Arithmetic Progression | Arithmetic Progression | CBSE | Class 10 | Maths | Maths | RD Sharma
2. Show that the sequence defined by an = 3n2 – 5 is not an A.P.

Solution:      

Given, {{a}_{n}}=3{{n}_{2}}-5          

Now putting n = 1, 2,3,4 we get,

{{a}_{1}}=3{{[1]}^{2}}-5=3-5=-2

{{a}_{2}}=3{{[2]}^{2}}-5=12-5=7

{{a}_{3}}=3{{[3]}^{2}}-5=27-5=22

{{a}_{4}}=3{{[4]}^{2}}-5=48-5=43

We can see that,

{{a}_{2}}-{{a}_{1}}=7-[-2]=9

{{a}_{3}}-{{a}_{2}}=22-7=15

{{a}_{3}}-{{\alpha }_{2}}=43-22=21

Since the difference between the terms is not common and varying, we can conclude that the given sequence defined by a<sub>n</sub> = 3n<sup>2</sup> - 5 is not an A.P.

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