Answer:
<em>x = 1 and -2</em>
<em>Sum of the first ten terms = 1,398,100</em>
Step-by-step explanation:
Given the geometric progression 2x+2, 16, 64x...
Since they are in GP, their common ratio is expressed as;
16/2x+2 = 64x/16
16/2(x+1) = 4x
8/x+1 = 4x
Cross multiply
4x(x+1) = 8
4x²+4x = 8
4x²+4x - 8 = 0
divide through by 4
x²+x - 2 = 0
Factorize
x²+2x-x- 2 = 0
x(x+2)-1(x+2) = 0
(x-1)(x+2) = 0
x = 1 and -2
Hence the values of x are 1 and -2
Get the common ratio;
r = 16/2x+2
Since x = 1
r = 16/2(1)+2
r = 16/4
r = 4
Sum of the first n terms is expressed as;
Sn = a(rⁿ-1)/r-1
a = 2x+2
a = 2(1)+2
a = 4
Substitute;
S10 = 4(4^10 - 1)/4 - 1
S10 = 4(1,048,576-1)/3
S10 = 4,194,300/3
S10 = 1,398,100
Hence the sum of the first ten terms is 1,398,100
Answer:
9x+4<m
Step-by-step explanation:
Answer:
hole at x=-3
Step-by-step explanation:
The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)
The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.
So anyways we have (x+3)/(x^2-9)
= (x+3)/((x-3)(x+3))
Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.
