Question

The first term of a geometric progression is 150 and the fourth is 1.2. Find the fifth term

Answer 1

Ответ:

b5=0.24

Пошаговое объяснение:

b4=b1*q³

1.2=150*q³

1=125*q³

q³=1/125

q=1/5

b5=$150*1/5^{4}$=150/625=0.24

Answer 2

To find the fifth term of a geometric progression (GP), you'll need to determine the common ratio (r) first, and then use that ratio to calculate the fifth term. The formula for the nth term of a geometric progression is:

$a_n = a_1 \cdot r^{(n-1)}$

Where:

• $a_n$ is the nth term.
• $a_1$ is the first term.
• $r$ is the common ratio.
• $n$ is the term number.

In your problem, you are given that the first term ($a_1$) is 150 and the fourth term ($a_4$) is 1.2. We can use this information to find the common ratio ($r$):

$a_4 = a_1 \cdot r^{(4-1)}$ $1.2 = 150 \cdot r^3$

Now, let's solve for $r$:

$r^3 = \frac{1.2}{150}$ $r^3 = 0.008$

Taking the cube root of both sides to find $r$:

$r = \sqrt[3]{0.008} \approx 0.2$

Now that you have found the common ratio ($r = 0.2$), you can use it to find the fifth term ($a_5$):

$a_5 = a_1 \cdot r^{(5-1)}$ $a_5 = 150 \cdot 0.2^4$

Now, calculate $a_5$:

$a_5 = 150 \cdot 0.2^4 = 150 \cdot 0.0016 = 0.24$

So, the fifth term of the geometric progression is 0.24.