1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ghella [55]
2 years ago
5

The third term in an arithmetic sequence is 9 and the fifth term is 21 . If the first term if a1, which is an equation for the n

th term of this sequence?
A:an=6n-9
B:an=14n+6
C:an=6n+14
D:an=9n-6
Mathematics
1 answer:
tino4ka555 [31]2 years ago
3 0

Answer:

A: an = 6n - 9

Step-by-step explanation:

third term in an arithmetic sequence is 9

a3 = a + 2d

a + 2d = 9

the fifth term is 21

a5 = a + 4d

a + 4d = 21

a + 2d = 9 (1)

a + 4d = 21 (2)

Subtract (1) from (2) to eliminate a

4d - 2d = 21 - 9

2d = 12

d = 12/2

d = 6

Substitute d = 6 into (1)

a + 2d = 9 (1)

a + 2(6) = 9

a + 12 = 9

a = 9 - 12

a = -3

nth term of this sequence = a + (n - 1)d

= -3 + (n - 1)6

= -3 + 6n - 6

= 6n - 9

an = 6n - 9

You might be interested in
Find the fraction equivalent to 8/24 in lowest term
olga2289 [7]
\frac{\big{8}}{\big{24}} = \frac{\big{8:8}}{\big{24:8}} = \frac{\big{1}}{\big{3}}
5 0
3 years ago
Read 2 more answers
Consider the sequence 8, 14, 20, 26, . . .. (a) What is the next term in the sequence? 2.2 Exercises 98 (b) Find a formula for t
omeli [17]

Answer:

Step-by-step explanation:

Each term of the given arithmetic sequence is 6 more than the previous one.  Thus, the next term is 26+6, or 32.

a(n) = 8 + 6(n-1)

3 0
3 years ago
Really need help with this pls help!!
worty [1.4K]

Let's carry this math sentence over to its natural, "shapey" element. We're going to look at each term not as an ordinary number, but as <em>the area of some shape</em>.

x² (read as "x <em>squared"</em>) can be seen as the area of a square with side lengths of x. 2x can similarly be seen as the area of a <em>rectangle </em>with a length of x and a width of 2. (Picture 1)

What's our question actually asking, though? Something about <em>perfect squares</em>. More specifically, we're looking for something to add on that'll <em>make this thing a perfect square</em>. We're trying to find a missing piece we can slot in to make a square, in other words. Problem is, our shapes don't look much like a square if we put them together right now. We need to do a little cutting and gluing first.

First, we're gonna cut the 2x rectangle lengthwise, getting two rectangles with an area of x, a length of 1, and a width of x. Next, we're going to attach them to the x² square, creating this shape that looks, strangely, like a square with a little bit missing from it (picture 2). What we're trying to do is <em>complete this square, </em>to find the area of that little missing chunk.

As it turns out, we have all the information we need for this. Notice that, using the lengths of the x rectangles, we can find that the square's dimensions are 1 x 1, which means that its area is 1 x 1  = 1.

If we tack this new area on to our original expression, we've "completed the square!" We now have a perfect square with side lengths of (x + 1) and an area of (x + 1)² (picture 3).

So, our final expression is x² + 2x + 1, and the missing constant - the area of the "missing square" we had to find to complete our larger one - is 1.

5 0
3 years ago
Read 2 more answers
Raymond wants to make a box that has a volume of 360 cubic inches. He wants the height to be 10 inches and the other two dimensi
Aleks [24]
V=LWH
h=10
V=360

360=LW10
divide both sides by 10
36=LW
try some values
ok so if we get L=1 and W=36, that is the same box as L=36 and W=1
so
L,W
36,1
18,2
12,3
9,4
6,6

5 of them

answer is 5 different boxes
dunno what the 'compare volume' is
8 0
3 years ago
Write a compound inequality for the graph shown below.<br> Use x for your variable.
ICE Princess25 [194]

Answer:

wheres your graph?

Step-by-step explanation:

i could do this with a graph lol

3 0
2 years ago
Read 2 more answers
Other questions:
  • What is the product of 3/5 of 40
    15·2 answers
  • Kenya pays $66.32 biweekly for health insurance , which is 18% of the total cost. Her employer pays the rest. What is the employ
    6·1 answer
  • A spinner has five equal sections that are numbered 1-5. In which distributions does the variable X have a binomial distribution
    10·1 answer
  • A rectangular box has dimensions 4 ft by 5 ft by 2 ft. Increasing each dimension of the box by the same amount yields a new box
    14·1 answer
  • HELP ME PLEASE ITS NOT THAT HARD
    15·1 answer
  • All zeros of polynomial function 3x^4 +14x^2 -5
    7·1 answer
  • Help me please, i am terrible at math
    11·2 answers
  • Someone please help T.T I need help ASAP
    11·1 answer
  • What is the value of log: 3 3
    7·1 answer
  • What is 5.271x10^-5 in standard form?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!