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Sergeeva-Olga [200]
3 years ago
5

What is the common ratio of the geometric sequence 16, 24, 36, 54, ...?

Mathematics
2 answers:
Marta_Voda [28]3 years ago
6 0

The common ratio for the geometric sequence is :
<span>32</span>

Explanation:

<span>16,24,36,54</span>

We calculate the common ratio r:
r is obtained by dividing a term by its preceding term

1) <span><span>2416</span>=<span>32</span></span>

2) <span><span>3624</span>=<span>32</span></span>

The common ratio for the geometric sequence is :
<span><span>32</span></span>

kompoz [17]3 years ago
3 0

Answer:  The required common ratio of the given geometric sequence is \dfrac{3}{2}.

Step-by-step explanation:  We are given to find the common ratio of the following geometric sequence :

16,   24,   36,   54,   .   .   .

We know that

the common ratio of a geometric sequence is the ratio of any term to its preceding term.

For the given sequence, we have

a(1) = 16,   a(2) = 24,  a(3) = 36,  a(4) = 54,  .  .  .

So, we get

\dfrac{a(2)}{a(1)}=\dfrac{24}{16}=\dfrac{3}{2},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{36}{24}=\dfrac{3}{2},\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{54}{36}=\dfrac{3}{2},~~.~~.~~.

Thus, the required common ratio of the given geometric sequence is \dfrac{3}{2}.

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