Question

fan and medal

Answer 1

Find the first six terms of the sequence. (1 point)

a1 = -6, an = 4 • an-1

0, 4, -24, -20, -16, -12
-24, -96, -384, -1536, -6144, -24,576
-6, -24, -20, -16, -12, -8
-6, -24, -96, -384, -1536, -6144
2. Find an equation for the nth term of the arithmetic sequence. (1 point)

-15, -6, 3, 12, ...

an = -15 + 9(n + 1)
an = -15 x 9(n - 1)
an = -15 + 9(n + 2)
an = -15 + 9(n - 1)
3. Find an equation for the nth term of the arithmetic sequence. (1 point)

a14 = -33, a15 = 9

an = -579 + 42(n + 1)
an = -579 + 42(n - 1)
an = -579 - 42(n + 1)
an = -579 - 42(n - 1)

Answer 2

question #1
we can write this:
using the definition of a_n, we have:
\[\begin{gathered}
{a_2} = 4{a_1} = ...? \hfill \\
{a_3} = 4{a_2} = ...? \hfill \\
{a_4} = 4{a_3} = ...? \hfill \\
{a_5} = 4{a_4} = ...? \hfill \\
{a_6} = 4{a_5} = ...? \hfill \\
\end{gathered} \]

Answer 3

In an arithmetic sequence, your formula is: \(a_n=a_1+(n-1)d\)

Answer 4

i have no idea... im so sorry

Answer 5

for example:
\[\Large \begin{gathered}
{a_2} = 4{a_1} = 4 \times \left( { - 6} \right) = - 24 \hfill \\
{a_3} = 4 \times \left( { - 24} \right) = ...? \hfill \\
{a_4} = 4{a_3} = ...? \hfill \\
{a_5} = 4{a_4} = ...? \hfill \\
{a_6} = 4{a_5} = ...? \hfill \\
\end{gathered} \]

Answer 6

what is a_3?

Answer 7

-９６

Answer 8

??

Answer 9

ok!
and waht is a_4=4*(-96)=...?

Answer 10

-384

Answer 11

??

Answer 12

ok!
and what is a_5= 4*(-384)=... ?

Answer 13

-1536??

Answer 14

that's right!

Answer 15

and what is a_6= 4*(-1536)=... ?

Answer 16

-6144, and net one is -24,576 :)

Answer 17

right ? :)

Answer 18

that's right!
So what is the right option?

Answer 19

-24, -96, -384, -1536, -6144, -24,576 :)

Answer 20

ok! :)

Answer 21

thank you :)
Do you think you can help me with 2 and 3?

Answer 22

yes!

Answer 23

2. Find an equation for the nth term of the arithmetic sequence. (1 point)

-15, -6, 3, 12, ...

an = -15 + 9(n + 1)
an = -15 x 9(n - 1)
an = -15 + 9(n + 2)
an = -15 + 9(n - 1)

Answer 24

as @Jhannybean well wrote, we have to apply this formula:
\[{a_n} = {a_1} + \left( {n - 1} \right)d\]

Answer 25

where a_1=-15, and d is the constant of our sequence.
Now d is equal to the difference between one term and its subsequent term, namely
\[d = - 6 - \left( { - 15} \right) = 3 - \left( { - 6} \right) = 12 - 3 = ...?\]

Answer 26

oops.. d is equal to the difference between ione term and its preceding term

Answer 27

so, what is d?

Answer 28

hint:
what is -6-(-15)=-6+15=... ?

Answer 29

+9 ??

Answer 30

that's right!

Answer 31

now, we have to insert that value into the above formula, so we can write:
\[{a_n} = {a_1} + \left( {n - 1} \right)d = {a_1} + 9\left( {n - 1} \right)\]

Answer 32

\[{a_n} = {a_1} + \left( {n - 1} \right)d = {a_1} + 9\left( {n - 1} \right) = - 15 + 9\left( {n - 1} \right)\]

Answer 33

okay. so it is an = -15 + 9(n - 1) ??

Answer 34

ok!

Answer 35

and i haveone more..... sorry

Answer 36

no worries :)

Answer 37

3. Find an equation for the nth term of the arithmetic sequence. (1 point)

a14 = -33, a15 = 9

an = -579 + 42(n + 1)
an = -579 + 42(n - 1)
an = -579 - 42(n + 1)
an = -579 - 42(n - 1)

Answer 38

here we have to apply the above formula, so we can write:
\[\begin{gathered}
{a_{14}} = {a_1} + \left( {14 - 1} \right)d \hfill \\
{a_{14}} = {a_1} + 13 \times d \hfill \\
- 33 = {a_1} + 13 \times d \hfill \\
\end{gathered} \]

Answer 39

and, we can write:
\[\begin{gathered}
{a_{15}} = {a_1} + \left( {15 - 1} \right)d \hfill \\
{a_{15}} = {a_1} + 14 \times d \hfill \\
9 = {a_1} + 14 \times d \hfill \\
\end{gathered} \]

Answer 40

is it ok?

Answer 41

no...lol

Answer 42

the general formula is:
\[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]

Answer 43

now, we set n=14, and we rewrite that formula, so we get:
\[\Large \begin{gathered}
{a_{14}} = {a_1} + \left( {14 - 1} \right)d \hfill \\
{a_{14}} = {a_1} + 13 \times d \hfill \\
- 33 = {a_1} + 13 \times d \hfill \\
\end{gathered} \]

Answer 44

now, is it ok?

Answer 45

not really... so what am I supposed to do???

Answer 46

we have to find a_1 and d

Answer 47

by definition, we can write:
\[\Large \begin{gathered}
{a_{15}} = {a_{14}} + d \hfill \\
9 = - 33 + d \hfill \\
\end{gathered} \]

Answer 48

so, what is d?

Answer 49

hint:
\[\Large d = 9 + 33 = ...?\]

Answer 50

４２！

Answer 51

that's right!

Answer 52

now we have to insert that value into the preceding formula:
\[\Large \begin{gathered}
- 33 = {a_1} + 13 \times d \hfill \\
- 33 = {a_1} + 13 \times 42 \hfill \\
- 33 = {a_1} + 546 \hfill \\
\end{gathered} \]

Answer 53

what is a_1?

Answer 54

hint:
\[\Large {a_1} = - 546 - 33 = ...?\]

Answer 55

−５７９？

Answer 56

ok!

Answer 57

now we have to substitute -579 in place of a_1 and 42 in place of d, into the general formula:
\[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]
what do you get?

Answer 58

an = -579 + 42(n - 1)　！！

Answer 59

well done! so, what is the right option?

Answer 60

an = -579 + 42(n - 1)　　haha thank you so much

Answer 61

thank you! :)

Answer 62

congratulations!! :)

Answer 63

thank you so much :)

Answer 64

thank you! :)

Answer 65

If you're done with the question, close it. It's distracting everyone.