Given:
The sequence is
1, 4, 16, 64
To find:
The general term of the given sequence.
Solution:
We have, the sequence
1, 4, 16, 64
Here, the ratio between two consecutive terms is same. So, it is a geometric sequence.
First term is:
Common ratio is:
The nth term of a geometric sequence is
...(i)
Where, a is the first term and r is the common ratio.
Putting a=1 and r=4 in (i), we get
Therefore, the general term of the given sequence is .
Answer:
Step-by-step explanation:
x = 8 ; y = 5/3
![\dfrac{1}{4}[x(2y+3z)] =\dfrac{1}{4}[8*(2*\dfrac{5}{3}+\dfrac{5}{3})]\\\\=\dfrac{1}{4}(8*(\dfrac{10}{3}+\dfrac{5}{3})]\\\\=\dfrac{1}{4}(8*\dfrac{15}{3})\\\\=\dfrac{1}{4}*8*5\\\\=2*5\\\\=10](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%5Bx%282y%2B3z%29%5D%20%3D%5Cdfrac%7B1%7D%7B4%7D%5B8%2A%282%2A%5Cdfrac%7B5%7D%7B3%7D%2B%5Cdfrac%7B5%7D%7B3%7D%29%5D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B4%7D%288%2A%28%5Cdfrac%7B10%7D%7B3%7D%2B%5Cdfrac%7B5%7D%7B3%7D%29%5D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B4%7D%288%2A%5Cdfrac%7B15%7D%7B3%7D%29%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B4%7D%2A8%2A5%5C%5C%5C%5C%3D2%2A5%5C%5C%5C%5C%3D10)
Answer:
1) Distance=Speed*time
90=(x+1)*(x)+(2x+5)(x-1)
90=x^2+x+2x^2-2x+5x-5
3x^2+4x-95=0
2) 3x^2+4x-95=0. Using quadratic formula, we get
x=(-4±sqrt(16-4*3*(-95)<u>)</u>)/6, x=5 or - 19/5 but since x also represents time, it can't be negative.
3) Total time take she took for the journey is x+x-1=2x-1=2*5-1=9 hours
Answer:
The answer is a). 5/24.
Step-by-step explanation:
For the seventh graders there are 4 Boys + 2 Girls which totals 6 students.
- The probability that a girl will be picked from the <em>seventh graders is 2/6</em>
For the eighth graders, there are 3 Boys + 5 Girls which totals 8 students
- The probability that a girl will be picked from the <em>eighth graders is 5/8</em>
To find the<u> probability that both are girls</u>, we multiply the two fractions together:
