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:
D
Step-by-step explanation:
The fourth term in an arithmetic sequence is 18 and the seventh term is 42. if the first term is a1, which is an equation for the nth term of this sequence?
1. an = 8n + 10
☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆ 2. an = 8n − 14
3. an = 16n + 10
4. an = 16n − 38
If you would like to know what was the original price of the shirt, you can calculate this using the following steps:
30% + 100% = 130%
130% of $22.40 = 130% * 22.40 = 130/100 * 22.40 = $29.12
The original price of the shirt was $29.12.
Answer:
(-5,-4)
Step-by-step explanation:
