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:
I don't know much about this but my teacher said it would be 16.48 or 164.8
Answer:
± 4i
Step-by-step explanation:
= 
= 
× ×
= 4i → [ = i ]
Katie, Let the number of nickles = N Since there are 7 more dimes than nickles, the number of dimes D = N + 7 Since there are 4 more quarters than nickles, the number of quarters Q = N + 4 Since quarters = $0.25, dimes = $0.10, and nickles = $0.05 and all added together = $4.90 ⇒ 0.25·Q + 0.10·D + 0.05·N = 4.90 Now multiply through by 100 to eliminate the decimal: 25Q + 10D + 5N = 490 Substitute for Q and D 25(N+4) + 10(N+7) + 5N = 490 25N + 10N + 5N +100 +70 = 490 40N + 170 = 490 ⇒ 40N = 320 ⇒ N = 320/40 N = 8, D = N+7 = 15 Q = N+4 = 12 Check: 25(12) + 10(15) + 5(8) = 300 + 150 + 40 = 490
10 - 0.33333333... = 9.6666666666...
in a fracion, it is 10 - 1/3 = 9 2/3
