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nata0808 [166]
4 years ago
15

find the sum of the geometric series -3,15,-75,375 when there are 9 terms and select the correct answer below

Mathematics
1 answer:
Oduvanchick [21]4 years ago
4 0
The sum to nterms:

Sn=a(r^n - 1) / (r-1)

r=15/-3=-5
a=-3

Sn=-3(-5⁹ - 1) / (-5-1)=-976563

Answer; -976563
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WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"
Feliz [49]

Recall Euler's theorem: if \gcd(a,n) = 1, then

a^{\phi(n)} \equiv 1 \pmod n

where \phi is Euler's totient function.

We have \gcd(9,32) = 1 - in fact, \gcd(9,32^k)=1 for any k\in\Bbb N since 9=3^2 and 32=2^5 share no common divisors - as well as \phi(9) = 6.

Now,

37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} =  32\cdot\left(32^{(\cdots)}\right)^6

where the c_i are positive integer coefficients from the binomial expansion. By Euler's theorem,

\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9

so that

32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9

7 0
2 years ago
The high temperature was recorded as 25.6°F. The low temperature that same day was recorded as −2.7°F. What was the difference b
VMariaS [17]

28.3

Step-by-step explanation:

the difference is the answer to a subtraction problem so we can plug in our numbers like this

25.6-(-2.7) which equals 28.3

a good thing to remember when subtracting negative numbers is that a positive and negative won't always make a negative like in this example

4 0
2 years ago
Please Help!!!
ValentinkaMS [17]
3 x 15 = 45
3 x 14 = 42

--------------

There are 14 packages.

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x = 42/3

-----> 3x=42
4 0
3 years ago
WILL GIVE BRAINLIST IF ANSWER IS CORRECT!
ella [17]

Answer: its is square pyramid or D

Step-by-step explanation:

5 0
3 years ago
Ron is 8 years old and 40 inches tall. If he grows at the same rate every year, how tall was he when he was 5 years old?
Vadim26 [7]
He would be 25 inches tall.

40 divided by 8 would equal 5 so at age 1, he was 5 inches tall. So 5 times 5 which is how old he was, would equal 25 inches.
5 0
3 years ago
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