Answer:
Option C. 1020
Step-by-step explanation:
From the question given above,
512 + 256 +... + 4 =?
We'll begin by calculating the number of terms in the sequence. This can be obtained as follow:
First term (a) = 512
Common ratio (r) = 2nd term / 1st term
Common ratio (r) = 256 /512
Common ratio (r) = 1/2
Last term (L) = 4
Number of term (n) =?
Tₙ = arⁿ¯¹
L = arⁿ¯¹
4 = 512 × (1/2)ⁿ¯¹
Divide both side by 512
4 / 512 = (1/2)ⁿ¯¹
1/128 = (1/2)ⁿ¯¹
Express 128 in index form with 2 as the base
1/2⁷ = (1/2)ⁿ¯¹
(1/2)⁷ = (1/2)ⁿ¯¹
Cancel 1/2 from both side
7 = n – 1
Collect like terms
7 + 1 = n
n = 8
Thus, the number of terms is 8
Finally, we shall determine the sum of the series as follow:
First term (a) = 512
Common ratio (r) = 1/2
Number of term (n) = 8
Sum of 8th term (S₈) = ?
Sₙ = a[1 – rⁿ] / 1 – r
S₈ = 512 [1 – (½)⁸] / 1 – ½
S₈ = 512 [1 – 1/256] ÷ ½
S₈ = 512 [255/256] × 2
S₈ = 2 × 255 × 2
S₈ = 1020
Thus, the sum of the series is 1020.
Answer:
45 square centimeters.
Step-by-step explanation:
Length(L) = 9 cm
breadth (b) = 5 cm
Area of the rectangle
= L * b
= 9 * 5
= 45 cm²
Hope it will help :)
Answer:
4 boxes
Step-by-step explanation:
the greatest number that you can divide all these numbers by equally is 4. There will be 9 chocolate, 13 red velvet, and 12 vanilla cupcakes in each box.
What triangle?? can you be more specific?
Answer:
Step-by-step explanation:
The area of a rectangle can be found with the equation 
, where 
is the length of the rectangle, and 
is the width.
From the problem statement, we know that 
. We also know that 
.
Plugging these numbers in, we get the following equation:
