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Anna11 [10]
3 years ago
5

What is the 6th term of the geometric sequence 4, −20, 100, ...?

Mathematics
2 answers:
shtirl [24]3 years ago
3 0
Let's calculate r of this G.P: (-20)/(4) = - 5(100)/(-20) = - 5So r = -5
The formula to find the nth term of a GP is;
a(n) = a(r)ⁿ⁻¹
<u />a₆ = a(r)⁶⁻¹
a₆ = 4(-5)⁵ = -12500<u />
Umnica [9.8K]3 years ago
3 0

Answer:

the 6th term of the given sequence is, - 12500

Step-by-step explanation:

The nth term for the geometric sequence is given by:

a_n = a_1 \cdot r^{n-1}      ....[1]

where,

a_1 is the first term

r is the common ratio of the terms.

Given the sequence:

4, −20, 100, ...

This is a geometric sequence.

Here,

a_1 =4 and r = -5

We have to find the 6th term of the given sequence:

Substitute n= 6 and the given values in [1] we have;

a_6 = 4 \cdot (-5)^5 = 4 \cdot -3125 = -12500

therefore, the 6th term of the given sequence is, - 12500

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Find x, y, and z<br><br> x = 39<br> x = 29<br> y = 61<br> y = 29<br> z = 61<br> z = 29
nikdorinn [45]

answer:

x = 29

y = 29

z = 61

step-by-step explanation:

all angles in a triangle must equal 180 degrees.

we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.

the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.

so to figure out y,

we must add 61+90 and then subtract the sum of that from 180.

so, 61+90 = 150 and 180-151 = 29

therefore,

we can conclude that y = 29

now, to determine the degrees of x and z we do the same thing.

we already know one angle equals 90 degrees.

180-90 = 90

that concludes that x and z must have a sum of 90.

if we use our choices,

39+61 = 100 (no)

39+29 = 68 (no)

29+61 = 90 (CORRECT)

29+29 = 28 (no)

<em>therefore, x = 29 and z = 61</em>

<em></em>

<em>so, in total :</em>

<em>x = 29</em>

<em>y = 29</em>

<em>z = 61</em>

<em></em>

<em>hope this helps :)   </em>

<em>-audrey <3 </em>

5 0
3 years ago
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