Question

1. GIven a sequence is defined by a first term of t1=3 and explicit definition tn=4n-1. Find the 4th term of the sequence

Answer 1

Answer:

$t_4=15$

x , 3-x , x , 3-x...

Step-by-step explanation:

Sequences

A sequence can be given as a general (iterative) or a recursive formula. The iterative formula allows us to find any term without computing any of the previous ones. The recursive formula needs to compute each term one by one until reaching to the desired term

1

The first sequence is defined as  

$t_n=4n-1$

$t_1=3$

To compute the fourth term, we set n=4 to get

$t_4=4(4)-1=15$

$\boxed{t_4=15}$

Please note we didn't need to know the value of the first term

2

We have the recursive formula

$t_{n+1}=(-1)t_n+3$

We are asked to describe the sequence. Let's recall we need at least one term to construct a recursive sequence. In this problem we don't have one, so we'll assume $a_1=5$. So

$a_2=(-1)(5)+3=-2$

$a_3=(-1)(-2)+3=5$

The sequence is 5,-2,5,-2,... it will repeat the same both terms forever

If we had chosen $a_1=x$

$a_2=(-1)(x)+3=3-x$

$a_3=(-1)(3-x)+3=x$

And the sequence will be x,3-x,x,3-x...