1. Find the 4th term for the sequence with formula tn= n² + 1

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1. Find the 4th term for the sequence with formula tn= n² + 1

for question 1, the answer is B for question 2, the answer is D

Step-by-step explanation:

1 C

2C

Step-by-step explanation:

Given a sequence is defined by a first term of LaTeX: t_1=3t 1 = 3, and explicit definition LaTeX: t_n=\:4n-1t n = 4 n − 1, find the 4th term of the sequence (i.e. LaTeX: t_4t 4).

Group of answer choices

this is is known as a linear sequence or arithmetic progression. Each term differs by certain value known as common difference

a deep dive into the solution

[tex]t_{1} =3 \\ t_{n} =4n-1[/tex]

when n=4

t4=4*4-1

t4=15

2.[tex]a_{n} =n^{2} -5[/tex]

when n=1

a1=1^2-5

a1=-4

when n=2

a2=2^2-5

a2=-1

when n=3

3^2-5

a3=4

when n=4

a4=4^2-5

11

when n=5

a5=5^2-5

a5=20

77

Step-by-step explanation:

im with everythinglos so yeahhhhh

step-by-step explanation:

[tex]The graph shows a distribution of data.what is the standard deviation of the data? a)0.5b)1.5c)2.0d)[/tex]

Step-by-step explanation:

the answer would be B, 105. -12,-3,6,15,24,33,42,51,60,69,78,87,96,105

15

Step-by-step explanation:

15

Step-by-step explanation:

The document you attached is appearing blurry on my screen but from what I could tell I think it may be the answer I stated above.

If you are trying to determine the 4th term you substitute n with 4.

4n-1

4(4)-1

16-1=15

These graph is cross the yaxis and x axis two ways.

[tex]Which statement is true regarding the graphed functions?[/tex]

[tex]t_4=15[/tex]

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

[tex]t_n=4n-1[/tex]

[tex]t_1=3[/tex]

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

[tex]t_4=4(4)-1=15[/tex]

[tex]\boxed{t_4=15}[/tex]

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

2

We have the recursive formula

[tex]t_{n+1}=(-1)t_n+3[/tex]

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 [tex]a_1=5[/tex]. So

[tex]a_2=(-1)(5)+3=-2[/tex]

[tex]a_3=(-1)(-2)+3=5[/tex]

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

If we had chosen [tex]a_1=x[/tex]

[tex]a_2=(-1)(x)+3=3-x[/tex]

[tex]a_3=(-1)(3-x)+3=x[/tex]

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

15

Step-by-step explanation:

JUST LEAR

17

Step-by-step explanation:

T4 = 4² + 1

T4 = 4² + 1 = 17

Yip yip that's all

[tex]1) 15\: 2)(-4,-1,11,20,...)[/tex]

Step-by-step explanation:

1) To find the 4th term given the Explicit Formula, i.e. definition, just plug it in. The common difference according to question is 4, the 1st term is 3.

[tex]t_{1}=3\\t_{n}=t_{1}+4(n-1)\\t_{n}=t_{1}+(n-1)d\\t_{4}=3+4(3)\\t_{4}=15[/tex]

2) For this another Sequence in Explicit definition we just need to plug it in:

[tex]a_{n}=n^{2}-5\\a_{1}=1^{2}-5 \Rightarrow a_{1}=-4\\a_{2}=2^{2}-5\Rightarrow a_{2}=-1\\a_{3}=3^{2}-5\Rightarrow a_{3}=4\\a_{4}=4^{2}-5\Rightarrow a_{4}=11\\a_{5}=5^{2}-5\Rightarrow a_{5}=20\\(-4,-1,11,20,...)[/tex]