For a sequence an=an-1+an-2 and a1=1, a2=2, find its first four terms

3, 5, 8, 13

Step-by-step explanation:

aₙ = aₙ₋₁ + aₙ₋₂

a₃ = a₂ + a₁ = 2 + 1 = 3

a₄ = a₃ + a₂ = 3 + 2 = 5

a₅ = a₄ + a₃ = 5 + 3 = 8

a₆ = a₅ + a₄ = 8 + 5 = 13

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.