All categories

3 years ago

Which rule can you use to find the nTH term of an arithmetic sequence in which the common difference is 5 and a12 = 63?

1 answer:

5 0

Arithmetic, nth = a + (n - 1)d, common difference, d = 5

a₁₂ = a + (12 -1)d = 63

a + 11d = 63

a + 11*5 = 63

a = 63 - 11*5

a = 63 - 55

a = 8

So the nth term = a + (n - 1)d = 8 + (n - 1)5

8 + 5*(n - 1)

8 + 5n - 5

8 - 5 + 5n

3 + 5n

So nth term = 3 + 5n

You might be interested in

Iteru [2.4K]

In order to find the equivalent expression, let's use the following property:

$a-(-b)=a+b$

In other words, when subtracting a negative number, we can just add the corresponding positive number, that is, switch the two negative signs for a positive sign.

So we have that:

$\begin{gathered} 18\frac{1}{5}-(-22\frac{2}{5})-(-40\frac{1}{5}) \\ =18\frac{1}{5}+22\frac{2}{5}+40\frac{1}{5} \end{gathered}$

Therefore the correct option is D.

8 0

5 months ago

Graph y=-6(3)^x please do the table and the graph 20 POINTS!

Margarita [4]

Answer:

Explanation to the answer below... (Answers in the Explanation)

Step-by-step explanation:

We Know that our rule is y = $y = -6(3)^{x}$ , which means we can use this rule to find y from x. Since we don't know what X, is, we have to assume numbers like 1, to 7. And there is no space to write on the graph, I'll put a virtual copy of a graph.

1st Point,

$y = -6(3)^{x}\\y = -6(3)^{1}\\y = -6(3)\\y = -18\\x = 1, y = -18$

2nd, point

$y = -6(3)^x\\ y = -6(3)^2\\y = -6(9)\\y = -54\\x = 2, y = -54$

3rd Point

$y = -6(3)^x\\y = -6(3)^3\\y = -6(27)\\y = -162\\x = 3, y = -162$

4th Point

$y = -6(3)^4\\y = -6(81)\\y = -486\\x = 4, y = -486\\$

5th Point

$y = -6(3)^5\\y = -6(243)\\y = -1458\\\x = 5, y = -1458$

6th Point

$y = -6(3)^x\\y = -6(3)^6\\y = -6(729)\\y = -4,374\\x = 6, y = -4,374\\$

7th Point (Last Point)

$y = -6(3)^x\\y = -6(3)^7\\y = -6(2,187)\\y. = -13,122\\x = 7, y = -13,122$

Let's now plot them on the Graph, the values are so big, the graph might look a little odd.

Always remember that we can continue the points infinitely, and there is no stop, The Graph is attached below...

4 0

2 years ago

24 cm ,18cm ,c We are looking for c

Ierofanga [76]

Step-by-step explanation:

we can find the value of c by Pythagoras theorem

according to Pythagoras theorem

h² = a² + b²

where

h = hypotenuse (i.e. longest side of a right angled triangle)

a = side

b = base

so, we have to find h or hypotenuse here

h² = (24)² + (18)²

h = 576 + 324 = 900

h² = √900 = 30

c = 30

therefore, value of c is 30.

Hope this answer helps you dear!

3 0

1 year ago

Solve y/2 + 22 =38 for y

KATRIN_1 [288]

Answer:

y = 32

Step-by-step explanation:

$\frac{y}{2}+22=38\\\frac{y}{2}=16\\y=32$

4 0

2 years ago

Read 2 more answers

Please need help in these 3 algebra questions !!!!

Marysya12 [62]

Answer:

$\large\boxed{7.\ B.\ 8s^2+16s+1}\\\\\boxed{8.\ D.\ -15t^9u^{11}}\\\\\boxed{11.\ C.\ 3,\ -2}$

Step-by-step explanation:

$7.\\(3s^2+7s+2)+(5s^2+9s-1)=3s^2+7s+2+5s^2+9s-1\\\\\text{combine like terms}\\\\=(3s^2+5s^2)+(7s+9s)+(2-1)\\\\=8s^2+16s+1$

$8.\\(-3t^2u^3)(5t^7u^8)=(-3\cdot5)(t^2t^7)(u^3u^8)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=-15t^{2+7}u^{3+8}=-15t^9u^{11}$

$11.\\n-the\ number\\\\n^2=n+6\qquad\text{subtract}\ n\ \text{and}\ 6\ \text{from both sides}\\\\n^2-n-6=0\\\\n^2+2n-3n-6=0\\\\n(n+2)-3(n+2)=0\\\\(n+2)(n-3)=0\iff n+2=0\ \vee\ n-3=0\\\\n+2=0\qquad\text{subtract 2 from both sides}\\n=-2\\\\n-3=0\qquad\text{add 3 to both sides}\\n=3$

4 0

3 years ago