Question

1,11,111,1111,..., Determine if the given sequences represent an AP, assuming that the pattern continues. If it is an AP, find the nth term.

Answer 1

use formula, $d_n=a_{n+1}-a_n$
In the above sequence,
a = 1;
d₁ = a₂–a₁ = 11–1 = 10
d₂ = a₃–a₂ = 111–11 = 100
d₃ = a₄–a₃ = 1111–111 = 1000

 As we know , in A.P the difference between the two consecutive terms is always constant
But the difference in sequence is not the same.
∴ The above sequence is not A.P

Answer 2

Given sequence :

1 , 11 , 111 , 1111, .....

a2 - a1 = 11 - 1 = 10

a3 - a2 = 111 - 11 = 100

Therefore ,

a2 - a1 ≠ a3 - a2

Difference between two

Successive terms are not equal.

Given sequence is not an A.P.

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