For a geometric sequence
<em>a</em>, <em>ar</em>, <em>ar</em> ², <em>ar</em> ³, …
the <em>n</em>-th term in the sequence is <em>ar</em> <em>ⁿ</em> ⁻ ¹.
The first sequence is
1, 3, 9, 27, …
so it's clear that <em>a</em> = 1 and <em>r</em> = 3, and so the <em>n</em>-th term is 3<em>ⁿ</em> ⁻ ¹.
The second sequence is
400, 200, 100, 50, …
so of course <em>a</em> = 400, and you can easily solve for <em>r</em> :
200 = 400<em>r</em> ==> <em>r</em> = 200/400 = 1/2
Then the <em>n</em>-th term is 400 (1/2)<em>ⁿ</em> ⁻ ¹.
Similarly, the other sequences are given by
3rd: … 4 × 2<em>ⁿ</em> ⁻ ¹
4th: … 400 (1/4)<em>ⁿ</em> ⁻ ¹
5th: … 5<em>ⁿ</em> ⁻ ¹
6th: … 1000 (1/2)<em>ⁿ</em> ⁻ ¹
7th: … 2 × 5<em>ⁿ</em> ⁻ ¹
Answer:
Step-by-step explanation:
18: 1, 2, 3, 6, 9, 18
66:, 1,2,3,6,11,22,33,66
the GCF is 6
If the square root of two more than a number is 9, the number is 71.
because the [square root of (x+2)]=9 than x=71
ANSWER
AB=76 BC=357 AC=365 This triangle is a right triangle.
EXPLANATION
We use the Pythagoras Theorem to determine whether the triangles are right triangles.
According to this theorem, the square of the hypotebuse is equal to the sum of the squares of the two shorter legs.
We have:
AB=76 BC=357 AC=365
133225=5776+127449
133225=133225
For the second triangle, we have;
B) Triangle ABC: AB=123 BC=836 AC=845
845²=123²+826²
714025=15129+682276
714025≠697405
The first triangle is a right triangle
Answer:
wrote the ordered pairs (5, 2.70), (11, 3.24), and (20, 4.05)
used two of the ordered pairs to find the slope
wrote the point-slope form for a linear equation
substituted the slope and the coordinates of one of the points to write the equation of the line
Step-by-step explanation:
