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Ostrovityanka [42]
3 years ago
5

Given the sequence 7, 14, 28, 56, ..., which expression shown would give the tenth term? 7^10 7•2^10 7•2^9

Mathematics
2 answers:
Goshia [24]3 years ago
5 0
Each term is 2 times the previous
geometric series

an=a1(r)^(n-1)
an=nth term
a1=first term
n=which term
r=common ratio

common ratio is 2
first term is 7
n=10

so
7(2)^(10-1)
7(2)^9

last option is the answer
Pie3 years ago
5 0

Answer:

7•2^9

Step-by-step explanation:

This is a geometric sequence, since each term is found by multiplying the previous term by 2.

The explicit formula for a geometric sequence is given by

a_n=a_1 \times r^{n-1}, where a₁ is the first term and r is the common ratio, and n is the term number.

For our sequence, the first term is 7.  The common ratio is 2.  This gives us

a_n=7 \times 2^{n-1}

Since we want the 10th term,

a_{10}=7 \times 2^{10-1}\\\\=7 \times 2^9

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First I converted the equation terms into sine and cosine.
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Substitution:
\frac{3sin^2\theta}{cos^2\theta} + \frac{7}{cos\theta} =3
Common Denominator Created:
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Multiply each term by the LCD:
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Substitution: Recall ⇒sin^2\theta =1-cos^2\theta 
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