Answer:
27/40
Step-by-step explanation:
This is the concept of sequences and series. To solve the question we proceed as follows:
2] T=-4n-3
to get the 11th term we substitute n=11 in the expression and simplify. Thus, plugging in n=11 we obtain:
T=-4(11)-3
T=-44-3
T=-47
thus the 11th term is -47
3] General term is T=n²-1. The 7th term will be evaluated as above:
plug in n=7 in the expression and simplify:
T7=7²-1
T7=49-1
T7=48
thus the 11th term is 48
4] General sequence is T=1/3n². The term will be evaluated as follows:
plug in n=3 in the expression and simplify:
T3=1/(3×3²)=1/27
Thus the 3rd term is 1/27
Answer:
x=27
Step-by-step explanation:
To evaluate the expression: ![[(3^{-5})(3^4)]^3](https://tex.z-dn.net/?f=%5B%283%5E%7B-5%7D%29%283%5E4%29%5D%5E3)
Step 1: Innermost group, apply the product of powers (
Therefore:
We then have:
![=[3^{-1}]^3](https://tex.z-dn.net/?f=%3D%5B3%5E%7B-1%7D%5D%5E3)
Step 2: Apply the power of a power
![[3^{-1}]^3=3^{-1 \times 3} =3 ^{-3}](https://tex.z-dn.net/?f=%5B3%5E%7B-1%7D%5D%5E3%3D3%5E%7B-1%20%5Ctimes%203%7D%20%3D3%20%5E%7B-3%7D)
Step 3: Apply the negative exponent
Step 4: Simplify
Therefore, the value of x in the simplified expression is 27.
