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liberstina [14]
3 years ago
8

Find the 8th term of the geometric sequence whose common ratio is 2/3 and whose first term is 7​

Mathematics
1 answer:
motikmotik3 years ago
8 0

Answer:

The 8th term of the sequence is 896/2187.

Step-by-step explanation:

We want to find the 8th term of a geometric sequence whose common ratio is 2/3 and whose first term is 7.

We can write a direct formula. Recall that the direct formula of a geometric sequence is given by:

\displaystyle x_{n} = a\left(r\right)^{n-1}

Where <em>a</em> is the initial term and <em>r</em> is the common ratio.

Substitute:

\displaystyle x_{n} = 7\left(\frac{2}{3}\right)^{n-1}

To find the 8th term, let <em>n</em> = 8. Substitute and evaluate:

\displaystyle \begin{aligned} x_{8} &= 7\left(\frac{2}{3}\right)^{(8) - 1} \\ \\ &= 7\left(\frac{2}{3}\right)^{7} \\ \\ &= 7\left(\frac{128}{2187}\right) \\ \\ &= \frac{896}{2187} = 0.4096...\end{aligned}

In conclusion, the 8th term of the sequence is 896/2187.

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Use this systems of equations to solve:

x = first antifreeze
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\left \{ {{.2x + .12y = .18(15)} \atop {x + y = 15}} \right.

Isolate y.

x + y = 15
Subtract x from both sides.
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Substitute y into the other equation.

.2x + .12(-x + 15) = .18(15)
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Answer:

Step-by-step explanation:

4 g.

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a=b=d

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a+a=180-42

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