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3 years ago

When finding the 9th term in a geometric sequence with a common ratio of 2 and a first

Mathematics

1 answer:

Zarrin [17]3 years ago

5 0

Answer:

Step-by-step explanation:

Nth term of a geometric sequence is given as:

$t_n = a r^{(n-1)}$ ...(1)

Plugging n = 9, a = 3 and r = 2 in the above equation, we find:

$t_9 = (3) (2)^{9-1}$

$t_9 = (3) (2)^{8}$ ... (2)

Comparing equations (1) & (2), we obtan:

(n - 1) = 8

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Use the diagram to find lengths. BP is the perpendicular bisector of AC. QC is the

faust18 [17]

Answer:

The length of the side PC is 34 cm.

Step-by-step explanation:

We are given that BP is the perpendicular bisector of AC. QC is the perpendicular bisector of BD. AB = BC = CD.

Suppose BP = 16 cm and AD = 90 cm.

As, it is given that AD = 90 cm and the three sides AB = BC = CD.

From the figure it is clear that AD = AB + BC + CD

So, AB = $\frac{90}{3}$ = 30 cm

BC = $\frac{90}{3}$ = 30 cm

CD = $\frac{90}{3}$ = 30 cm

Since the triangle, BPC is a right-angled triangle as $\angle$ PBC = 90°, so we can use Pythagoras theorem in this triangle to find the length of the side PC.

Now, the Pythagoras theorem states that;

$\text{Hypotenuse}^{2} = \text{Perpendicular}^{2} +\text{Base}^{2}$

$\text{PC}^{2} = \text{BP}^{2} +\text{BC}^{2}$

$\text{PC}^{2} = \text{16}^{2} +\text{30}^{2}$

$\text{PC}^{2} = 256+900$ = 1156

$\text{PC}=\sqrt{1156}$

PC = 34 cm

Hence, the length of the side PC is 34 cm.

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3 years ago

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umka2103 [35]

Answer:

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The first step is to find the GCF. Here, it's 3.

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To find the factors, you will need to find 2 numbers that add to -7, and multiply to 10. -2 and -5 add to -7 and multiply to 10. Now, replace -7a with the factors.

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