Question

What is a30 for the arithmetic sequence presented in the table below?

n 6 11
an 50 35


Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.

a30 = −42
a30 = −38
a30 = −28
a30 = −22
Post New Answer

Answer 1

can you help me please? @mathmale

Answer 2

Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference. Neither a1 nor d is given; we have to find both. Fortunately, we are given two examples: when n=6, an=50, and when n=11, an=35.

Answer 3

yeah thats what i did but i got these huge numbers

Answer 4

an = a1 + d(n − 1)

Let's substitute 50 for an and 6 for n: an = 50 + d(6 − 1)

Answer 5

so it would be an = 50 + 5d right?

Answer 6

an = a1 + d(n − 1) now subst. 35 for an and 11 for n. Type out your result, please.

Answer 7

and an = 35 + 10d?

Answer 8

so it would be an = 50 + 5d right?

try it! let n=6. But there's no "n" in your equation.

Answer 9

You need an equation for an that depends upon a1 and n.

To obtain such an equation you must have a1 and d.

What have you done so far to find a1 and d?

Answer 10

no there isn't an n

Answer 11

im confused on how to do the equation

Answer 12

Then your formula won't function as it should.

If you had the correct formula, I could give y ou "n=6" and your formula would return 50. Know why that is?

Answer 13

no i don't, why is that?

Answer 14

You are told that if n=6, an=a6=50, right?

Answer 15

yess

Answer 16

and you are told that if n=11, an=a11=35. Right?

Answer 17

so what do i do

Answer 18

I was going thru the procedure of helping you set u p 2 equations from which you could obtain a1 and d. But you typed, "so it would be an = 50 + 5d right?"

You might need to develop some patience here.

Answer 19

Starting over with the general formula: an=a1+d(n-1).

Case 1: when n=6 an =50.

The general formula becomes 50=a1+d(6-1), or 50=a1+d(5).

Case 2: when n=11, an=35.

the general formula then becomes what?

Answer 20

Making any progress?

Answer 21

35= a1+d(11-1)

Answer 22

or d(10)

Answer 23

Better yet, a1+10d=35.

What was the other equation?

Answer 24

a1+5d=50

Answer 25

but how do i get the answer from these 2 equations

Answer 26

Yes. Now please solve these 2 equations simultaneously.
You could find either d or a1.

What methods have you used in the past to solve simultaneous linear equations?

Answer 27

by solving them do i divide?

Answer 28

like 35 divided by 10 and 50 divided by 5?

Answer 29

No. You'll need to eliminate one variable and then find the other.

Which var. do you want to find first, d or a1?

Answer 30

a1

Answer 31

You have 2 equations: a1+5d=50 and a1+10d=35

How would you eliminate the variable d, so that you could find the value of a1?

Answer 32

multiplying ?

Answer 33

i really wanna figure this out fast because I'm timed in my assignment please and i just need this one question i don't understand @mathmale

Answer 34

Commonly used methods include
1) addition/subtraction; 2) substitution; 3) graphing.

Answer 35

You have 2 equations: a1+5d=50 and a1+10d=35
Multiply the 1st one by -2 and write out your result here.

Answer 36

multply -2 to what

Answer 37

-2(a1+5d=50) = ??

Answer 38

Multiply the first equation by -2.

Answer 39

Result?

Answer 40

where did you get the -2 from?

Answer 41

I'll explain that later if you like. You sound like you're in a hurry. Let's solve the problem and then come back to discuss the details.

Answer 42

By the way, the method we're using here is the "addition / subtraction method."

Answer 43

-2(a1+5d=50) = -2a1 -10d = -100

Answer 44

Can you see how I obtained that?

If so, combine your two equations:

Answer 45

2a1 -10d = -100
a1 + 10d = 35
----------------

???

Answer 46

a(30)=65-3(30-1) so we solve for a(30)

Answer 47

so its -22

Answer 48

Excuse me, that should be

-2a1 -10d = -100
a1 + 10d = 35
----------------

Answer 49

Add each colum separately.

Combine:

-2a1
+a1
-----
?

Answer 50

Hint: -2 + 1 = -1

Hint #2: -2k + 1k = -1k

Answer 51

I'm sorry this is going slowly. My goal is to help you understand this material, as well as to finish the problem in time to get credit for it.

OpenStudy says you're "just looking around." I need your full attention.

Answer 52

a(30)=65-3(30-1) so we solve for a(30) is correct. Why didn't you say you had tentatively arrived at a conclusion?

What's your final answer? a(30)= ?