Question

Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = -226.

-334
-274
-284
-346

Answer 1

hint:
we can write these equations:
\[\Large \begin{gathered}
{a_{22}} = {a_1} + 21d \hfill \\
{a_{31}} = {a_1} + 30d \hfill \\
\end{gathered} \]
since the general formula is:
\[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]
where d is the constant of your sequence

Answer 2

using your data we can rewrite the first equation as follows:
\[\Large - 226 = 26 + 21d\]
please solve that equation for d

Answer 3

-252=21d
d=-12

Answer 4

is that right

Answer 5

that's right!

Answer 6

now, substituting that value of d into the second equation, we get:
\[\Large {a_{31}} = 26 + 30 \times \left( { - 12} \right) = ...?\]

Answer 7

-344

Answer 8

Thanks!

Answer 9

that's right!

Answer 10

:)

Answer 11

Given the functions f(n ) = 11 and g(n ) = -2(n - 1), combine them to create an arithmetic sequence, an, and solve for the 31st term.

an = 11 - 2(n - 1); a31 = -49
an = 11 - 2(n - 1); a31 = -51
an = 11 + 2(n - 1); a31 = 71
an = 11 + 2(n - 1); a31 = 73

Answer 12

can u help me with this one

Answer 13

ok!

Answer 14

for example, let's consider the first option:
we have:
\[\Large {a_n} = 11 - 2\left( {n - 1} \right)\]
so for n=31, we can rewrite that equationas follows:
\[\Large {a_{31}} = 11 - 2 \times \left( {31 - 1} \right) = ...?\]
please continue

Answer 15

a31= -49 right?

Answer 16

yes! that's right!

Answer 17

Thanks

Answer 18

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.

n an
1 40
2 47
3 54

Answer 19

can u help me with this one

Answer 20

Those are the options:

an = 40 + 7(n - 1) where n ≥ 40
an = 40 + 7(n - 1) where n ≥ 1
an = 40 - 7(n - 1) where n ≥ 40
an = 40 - 7(n - 1) where n ≥ 1

Answer 21

Please wait:
also the third option is correct, since we can write this:
\[\Large {a_{31}} = 11 + 2 \times \left( {31 - 1} \right) = ...?\]

Answer 22

Oh

Answer 23

a31=11+2×(31−1)= 71

Answer 24

yes!

Answer 25

71 is not an answer option tho

Answer 26

Oh yes it is nevermind

Answer 27

Which one is the right one? How can I know?

Answer 28

I'm pondering...

Answer 29

Do I just make a guess?

Answer 30

maybe the first one, since the first option contains both f(n) and g(n), whereas the third option contains f(n) and -g(n)

Answer 31

Okay thanks!

Answer 32

:)

Answer 33

can u help me with thise one now:

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.

n an
1 40
2 47
3 54

Those are the options:

an = 40 + 7(n - 1) where n ≥ 40
an = 40 + 7(n - 1) where n ≥ 1
an = 40 - 7(n - 1) where n ≥ 40
an = 40 - 7(n - 1) where n ≥ 1

Answer 34

ok!

Answer 35

the constant of your sequence is:
\[d = 47 - 40 = 54 - 47 = ...?\]

Answer 36

d=7

Answer 37

that's right!

Answer 38

:)

Answer 39

so, since the general formula, is:
\[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]
replace a_1 with 40 and d with 7, what do you get?

Answer 40

an=40+(n−1)7

Answer 41

whats in the n spot?

Answer 42

n is the number of terms, it is a natural number, more precisely
n-1 is the number of terms of the sequence which precede a_n

Answer 43

Okay so is the answer the second one

Answer 44

yes! since we start to count from n=1

Answer 45

THANKS!

Answer 46

:)