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marin [14]
3 years ago
14

What is the value of y in the sequence below 2, У, 18,-54, 162

Mathematics
1 answer:
Maslowich3 years ago
3 0

Answer:

<em>y=-6</em>

Step-by-step explanation:

<em>Geometric Sequences</em>

Any given sequence is said to be geometric if each term a_n can be obtained as the previous term a_{n-1} by a constant value called the common ratio.

a_n=a_{n-1}.r

or equivalently

a_n=a_1.r^{n-1}

Looking closely at the sequence 2, y, 18,-54, 162 we can try to find out if it's a geometric sequence or not. We compute the possible common ratios

\displaystyle \frac{162}{-54},\ \frac{-54}{18} and we see they both result -3. If we use r=-3 and try to find the second term (y), then

y=2*(-3)=-6

Now we compute the third term: (-6)(-3)=18

Since we got the third term as given in the original sequence.

So y=-6

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