Answer:
![a_5 = 32](https://tex.z-dn.net/?f=a_5%20%3D%2032)
Step-by-step explanation:
The nth term for the geometric sequence is given by:
![a_n = a_1 \cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1%20%5Ccdot%20r%5E%7Bn-1%7D)
where,
is the first term
r is the common ratio
n is the number of terms.
As per the statement:
For the geometric sequence of
and r=2
We have to find ![a_5](https://tex.z-dn.net/?f=a_5)
for n = 5;
![a_5=a_1 \cdot r^{n-1}](https://tex.z-dn.net/?f=a_5%3Da_1%20%5Ccdot%20r%5E%7Bn-1%7D)
Substitute the given values we have;
![a_5 = 2 \cdot 2^4 = 2 \cdot 16](https://tex.z-dn.net/?f=a_5%20%3D%202%20%5Ccdot%202%5E4%20%3D%202%20%5Ccdot%2016)
⇒![a_5 = 32](https://tex.z-dn.net/?f=a_5%20%3D%2032)
Therefore, the value of
is, 32
1st drop(.71) 2nd drop(-1.22)
Step 1 : Simplify both sides
-5(6a+21)=-15
(-5)(6a)+(-5)(21)=-15
-30a-105=-15
Step 2 : Add 105 to both sides
-30a-105+105=-15+105
-30a=90
Step 3 : Divide both sides by -30
-30a=90
—————
-30 -30
a = -3
The mathematical sentence can be written as:
x^3 = y^5
<h3>
How to write the expression?</h3>
A number a to the power of n is written as:
a^n
Then:
"x to the power of 3 is equal to y to the power of 5"
Would be written as:
x^3 = y^5
Particularly, this does not appear in the given options, but this is the correct and simplest way of writing the given mathematical sentence.
If you want to learn more about expressions, you can read:
brainly.com/question/4344214