Find the 70th term of the following arithmetic sequence.
13, 22, 31, 40,

634

Step-by-step explanation:

Nth term of an arithmetic progression is given by:

Tn=a+(n-1)d

Where 'Tn' is the Nth term of A.P. , 'a' is the first term of A.P. , 'n' is the no. of terms and 'd' is the common difference.

22-13=9, 31-22=9, 40-31=9.

So, d=9

a=13

n=70

Put the values in the Formula.

T70=13+(70-1)*9=13+69*9=13+621=634

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80