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galina1969 [7]
3 years ago
6

For the series 16, 24, 36, 54,... find S7.

Mathematics
1 answer:
diamong [38]3 years ago
5 0
24 - 16 = 8
36 - 24 = 12
54 - 36 = 18

So, obviously, this isn't an arithmetic sequence.

24/16 = 3/2
36/24 = 3/2
54/36 = 3/2

Aha! This is a geometric sequence.

Now, let's find the 7th term in this sequence!

a_n = a_1 \cdot r^{n-1}

We're trying to solve for a_7.
We know that a_1 is 16
We know that n = 7
We know that r = 3/2 or 1.5

Plug it in!

a_n = a_1 \cdot r^{n-1}\\\\a_7 =16 \cdot 1.5^{7-1}\\\\a_7 = 16 \cdot 1.5^6\\\\a_7 = 16 \cdot 11.390625\\\\\boxed{\bf{ a_7 = 182.25}}

The seventh term is 182.25
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Draw a diagram!  Lets say the width is x, then the length must be 2x.
   
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7 0
3 years ago
Are there less than 1 million, exactly 1 million, or greater than 1 million milligrams in 1 kilogram? Explain how you know
NISA [10]
It is exactly one million milligrams
5 0
3 years ago
Read 2 more answers
Write in simplest form:<br> <img src="https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B24a%5E%7B10%7Db%5E%7B6%7D%7D" id="TexFormula1" ti
Charra [1.4K]

Answer:

2a^3b^2\sqrt[3]{3a}

Step-by-step explanation:

Use the following rules for exponents:

a^m*a^n=a^{m+n}\\\\\sqrt[3]{x^3}=x

Simplify 24. Find two factors of 24, one of which should be a perfect cube:

8*3=24\\\\2^3=8

Insert:

\sqrt[3]{2^3*3a^{10}b^6}

Now split the exponents. Split 10 into as many 3's as possible:

10=3+3+3+1

Insert as exponents:

\sqrt[3]{2^3*3*a^3*a^3*a^3*a^1*b^6}

Split 6 into as many 3's as possible:

6=3+3

Insert as exponents:

\sqrt[3]{2^3*3*a^3*a^3*a^3*a^1*b^3*b^3}

Now simplify. Any terms with an exponent of 3 will be moved out of the radical (rule #2):

2\sqrt[3]{3*a^3*a^3*a^3*a^1*b^3*b^3}\\\\\\2*a*a*a\sqrt[3]{3*a^1*b^3*b^3}\\\\\\2*a*a*a*b*b\sqrt[3]{3*a^1}

Simplify:

2a^3b^2\sqrt[3]{3a}

:Done

6 0
3 years ago
Bianca's bank offers a savings account with a 2.1% APR, compounded monthly. What is the actual annual percentage yield on this a
Elanso [62]
2.1 x 12 = 25.2% is the percentage yield
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3 years ago
Read 2 more answers
What is 4and1/2 subtract 1/4
umka21 [38]

4 1/2=4 2/4

4 2/4-1/4=4 1/4 or 4.25

8 0
3 years ago
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