Question

The sequence a1, a2, …., an has the property that every term beginning with the third is the sum of the previous two i.e. an = an – 2 + an –1 for n ≥ 3. Let a9 = 110 and a7 = 42 then

Answer 1

Given : The sequence a₁, a₂, …., aₙ has the property that every term beginning with the third is the sum of the previous two

i.e. aₙ= aₙ₋₂+ aₙ₋₁ for n ≥ 3.

a₉ = 110 and a₇ = 42

To Find : Sequence

Solution:

aₙ= aₙ₋₂+ aₙ₋₁ for n ≥ 3.

n = 9

=> a₉ = a₇ + a₈

=> 110 = 42 + a₈

=> a₈ = 68

n = 8

=> a₈ = a₆ + a₇

=> 68 = a₆ + 42

=>  a₆ = 26  and  so  on

Sequence is

2,  4 , 6 , 10 , 16 , 26  ,  42 ,  68 , 110

a₁ = 2   , a₂ = 4

and aₙ= aₙ₋₂+ aₙ₋₁ for n ≥ 3.

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