Question

Show that the sequence defined by $a_{n}=3n^{2}-5$ is not an A.P.,

Answer 1

Answer:

The given sequence is not an A.P.

Step-by-step explanation:

Given :

3n² - 5 …………(1)

On putting n = 1 in eq 1,

a1 = 3(1)² – 5

a1 = 3 - 5

a1 = -2

On putting n = 2 in eq 1 ,

a2 = 3(2)² – 5

a2 = 3 × 4 - 5

a2 = 12 – 5

a2 = 7

 

On putting n = 3 in eq,

a3  = 3(3)² – 5

a3  = 3 × 9  - 5

a3 = 27 - 5

a3 = 22

 

Common difference, d1 = a2 – a1

d1= 7 – (-2)  

d1 = 7 +2

d1 = 9

 

Common difference, d2 = a3 – a2

d2 = 22 – 7

d2 = 15

Since, Common difference d1 & d2 are not  equal i.e d1 ≠ d2 .

Hence, the given sequence is not an A.P.

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Answer 2

Answer:

Step-by-step explanation:

When n = 1

3*1 - 5 = -2

when n = 2

3*4-5= 7

when n = 3

3*9-5 = 22

since the difference between the terms r not equal

hence they r not in AP