2.)which sequences could be described by the recursive definition latex: a_{n+1}=3\cdot a_n-1a n + 1 = 3 ⋅ a n − 1

3.)given that the first term is latex: t_1=2t 1 = 2, and the recursive definition is latex: t_{n+1}=3^{\left(t_n\right)}t n + 1 = 3 ( t n ), what would be the 2nd term (latex: t_2t 2).

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Question 1

Consider the sequence:

8, 11, 14, 17, 20, 23, 26, ...

Write a recursive definition.

Question 2

Which sequences could be described by the recursive definition

2, 5, 14, 41, 122...

Question 3

Given that the first term is and the recursive definition is would be the 2nd term

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.