Given a sequence is defined by the explicit definition latex: t_n=\: n^2+nt n = n 2 + n, find the 4th term of the sequence. (ie latex: t_4t 4)

3,5,9,17,33

Step-by-step explanation:

The explicit definition is;

When n=1, we get:

When n=2, we obtain:

When n=3, we get:

When n=4, we get:

When n=5, we obtain:

The sequence generated is 3,5,9,17,33,...

The third choice is correct.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.

∠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.