Question

a1 = 4, an = 4an−1, n > 1 then a100 mod 7 = ................

(a) 2 (b) 3 (c) 4 (d) 5
​

Answer 1

Answer:

i think the answer is (d) five

Answer 2

Given : a₁ = 4 , aₙ = 4aₙ₋₁  n > 1

To Find : a₁₀₀ mod 7  

(a) 2 (b) 3 (c) 4 (d) 5

Solution:

a₁ = 4

aₙ = 4aₙ₋₁

=> a₂ = 4(4) = 16 = 4²

a₃ = 4a₂  = 4(16) = 64 = 4³

a₄ = 4a₃  = 4(4³) =   4⁴

aₙ = 4ⁿ

a₁₀₀ = 4¹⁰⁰

4¹⁰⁰

=  4⁹⁹.4¹

= (4³)³³.4

= (64)³³.4

= (63 + 1)³³.4

63 mod 7 = 0

= ( 1)³³.4

= 4

a₁₀₀ mod 7 = 4

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