Because the difference between any term and the previous term is a constant, this is an arithmetic sequence because of that constant which is referred to as the common difference, d. Which in this case is -35--38=-32--35=3
Any arithmetic sequence can be expressed as:
a(n)=a+d(n-1), a=initial term, d=common difference, n=term number.
In this case a=-38 and d=3 so
a(n)=-38+3(n-1) which we can simplify to
a(n)=-38+3n-3
a(n)=3n-41, so the 52nd term is:
a(52)=3(52)-41
a(52)=156-41
a(52)=115
Given:
The expression is
![\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B48%7D%3D%5Csqrt%5B3%5D%7B8%5Ccdot%20%5C_%5C_%7D%3D)
To find:
The simplified form of the expression.
Solution:
We have,
![\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B48%7D%3D%5Csqrt%5B3%5D%7B8%5Ccdot%20%5C_%5C_%7D%3D)
The expression
can be written as
![\sqrt[3]{48}=\sqrt[3]{8\cdot 6}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B48%7D%3D%5Csqrt%5B3%5D%7B8%5Ccdot%206%7D)
![[\because \sqrt[3]{ab}=\sqrt[3]{a}\sqrt[3]{b}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csqrt%5B3%5D%7Bab%7D%3D%5Csqrt%5B3%5D%7Ba%7D%5Csqrt%5B3%5D%7Bb%7D%5D)
![\sqrt[3]{48}=2\cdot \sqrt[3]{6}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B48%7D%3D2%5Ccdot%20%5Csqrt%5B3%5D%7B6%7D)
![\sqrt[3]{48}=2\sqrt[3]{6}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B48%7D%3D2%5Csqrt%5B3%5D%7B6%7D)
Therefore,
.
Answer:
-15
Step-by-step explanation:
Given is a polynomial in x

We have to find the remainder when the above polynomial is divided by x+5
Remainder theorem says that f(x) gives remainder R when divided by polynomial x-a means f(a) = R
Applying the above theorem we can say that value of the function when x =-5
= Remainder when f is divided by x+5
= F(-5)
Substitute the value of -5 in place of x
= (-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70
= 625-1500+750+60+70
= 5
Hence answer is 5