Type the correct answer in each box. Use sigma notation to represent the following series for the first 10 terms. 3 + (-6) + 12
+ (-24) + ⋯
1 answer:
Answer:
Kindly check attached picture
Step-by-step explanation:
Given the following :
First term (a) = 3
Second term = - 6
third term = 12
Fourth term = - 24
We can obtain the common ratio of the series using the relation :
(2nd term/ 1st term) = (3rd term/2nd term) = (4th term/ 3rd term) =....
(-6/3) = (12/-6) = (-24/12)
-2 = - 2 = - 2
Further explanation can be found in attached picture
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Answer:
The expressions which equivalent to are:
⇒ B
⇒ C
Step-by-step explanation:
Let us revise some rules of exponent
×
=
Now let us find the equivalent expressions of
A.
∵ 4 = 2 × 2
∴ 4 =
∴ =
- By using the second rule above multiply 2 and (n + 2)
∵ 2(n + 2) = 2n + 4
∴ =
B.
∵ 4 = 2 × 2
∴ 4 = 2²
∴ = 2² ×
- By using the first rule rule add the exponents of 2
∵ 2 + n + 1 = n + 3
∴ =
C.
∵ 8 = 2 × 2 × 2
∴ 8 = 2³
∴ = 2³ ×
- By using the first rule rule add the exponents of 2
∵ 3 + n = n + 3
∴ =
D.
∵ 16 = 2 × 2 × 2 × 2
∴ 16 =
∴ =
×
- By using the first rule rule add the exponents of 2
∵ 4 + n = n + 4
∴ =
E.
is in its simplest form
The expressions which equivalent to are:
⇒ B
⇒ C
Given:
Line a is perpendicular to line b .
Line a passes through the points (1,-8) and (9,-12) .
Line b passes through the point (-8, -16).
To find:
The equation of b.
Solution:
Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is
Product of slopes of two perpendicular lines is -1.
Slope of line b is 2.
If a line passing through a point with slope m, then equation of line is
Line b passing through (-8,-16) with slope 2. So, equation of line b is
Subtract 16 from both sides.
Therefore, the equation of line b is .