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1 year ago

Find the area of a circle with radius r = 6 cm

1 answer:

5 0

The formula to find the area of a circle is pi x radius^2.

pi = 3.14 (in this case)
radius = 6

6^2 (6 x 6) = 36

36 x 3.14 (radius^2 x pi) = 113.04

So, the area of a circle with radius 6 cm is 113.04 cm.

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Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?

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Answer:

$a_n = 16(\frac{1}{4})^{n - 1}$

Step-by-step explanation:

Given:

Fifth term of a geometric sequence = $\frac{1}{16}$

Common ratio (r) = ¼

Required:

Formula for the nth term of the geometric sequence

Solution:

Step 1: find the first term of the sequence

Formula for nth term of a geometric sequence = $ar^{n - 1}$ , where:

a = first term

r = common ratio = ¼

Thus, we are given the 5th term to be ¹/16, so n here = 5.

Input all these values into the formula to find a, the first term.

$\frac{1}{16} = a*\frac{1}{4}^{5 - 1}$

$\frac{1}{16} = a*\frac{1}{4}^{4}$

$\frac{1}{16} = a*\frac{1}{256}$

$\frac{1}{16} = \frac{a}{256}$

Cross multiply

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Divide both sides by 16

$\frac{256}{16} = \frac{16a}{16}$

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$a = 16$

Step 2: input the value of a and r to find the nth term formula of the sequence

nth term = $ar^{n - 1}$

nth term = $16*\frac{1}{4}^{n - 1}$

$a_n = 16(\frac{1}{4})^{n - 1}$

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