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

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

## This Post Has 12 Comments

1. jonquil201 says:

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

Step-by-step explanation:

2. steffweikeloyrt00 says:

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

$t_{1} =3 \\ t_{n} =4n-1$

when n=4

t4=4*4-1

t4=15

2.$a_{n} =n^{2} -5$

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

3. JBBunny says:

77

Step-by-step explanation:

4. Expert says:

im with everythinglos so yeahhhhh

step-by-step explanation:

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

5. nila173 says:

Step-by-step explanation:

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

6. dugg5361 says:

15

Step-by-step explanation:

7. londonval says:

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

8. Expert says:

These graph is cross the yaxis and x axis two ways.
$Which statement is true regarding the graphed functions?$

9. stella013108 says:

$t_4=15$

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...

10. pumaben2864 says:

15

Step-by-step explanation:

JUST LEAR

11. laneycasey5375 says:

17

Step-by-step explanation:

T4 = 4² + 1

T4 = 4² + 1 = 17

Yip yip that's all

12. aramirez4785 says:

$1) 15\: 2)(-4,-1,11,20,...)$

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.

$t_{1}=3\\t_{n}=t_{1}+4(n-1)\\t_{n}=t_{1}+(n-1)d\\t_{4}=3+4(3)\\t_{4}=15$

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

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