PLEASE HURRY Find the sum of the first 10 terms in the series: -3, 9, -27, 81... a. -14763 c. 44286 b. 4920 d. 59049
2 answers:
Answer:
Step-by-step explanation:
-3, 9, -27, 81...
The common ratio can be found by taking the quotient of a term in the sequence and the previous term.
The common ratio is -3.
A term in the sequence multiplies itself by -3 to get the next term.
The nth term for the sequence is :
The first 10 terms of the sequence are :
-3, 9, -27, 81, -243, 729, -2187, 6561, -19683, 59049
Adding these 10 terms :
-3 + 9 + -27 + 81 + -243 + 729 + -2187 + 6561 + -19683 + 59049
⇒ 44286
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Answer: By the slope formula.
Step-by-step explanation:
Given: ABC is a triangle (shown below),
In which A≡(6,8), B≡(2,2) and C≡(8,4)
And, D and E are the mid points of the line segments AB and BC respectively.
Prove: DE║AC and DE = AC/2
Proof:
Since, And, D and E are the mid points of the line segments AB and BC respectively.
Therefore, By mid point theorem,
coordinate of D are
Coordinate of E are
By the distance formula,
By the slope formula,
Slope of AC =
Slope of DE =
Statement Reason
1. The coordinate of D are (4,5) and 1. By the midpoint formula
the coordinate of E are (5,3)
2. The length of DE = √5 2. By the Distance formula
The length AC = 2√5 ⇒ Segment DE
is half the length of segment AC
3. The slope of DE = -2 and the 3. By the slope formula
slope of AC = -2
4. DE║AC 4. Slopes of parallel lines are equal
