Answer:
Ai. Common ratio = 2/3
Aii. First term = 54
B. Sum of the first five terms = 422/3
Step-by-step explanation:
From the question given above, the following data were obtained:
3rd term (T3) = 24
6Th term (T6) = 64/9
First term (a) =?
Common ratio (r) =?
Sum of the first five terms (S5) =?
Ai. Determination of the common ratio (r).
T3 = ar²
T3 = 24
24 = ar²....... (1)
T6 = ar⁵
T6 = 64/9
64/9 = ar⁵......... (2)
The equation are:
24 = ar²....... (1)
64/9 = ar⁵......... (2)
Divide equation 2 by equation 1.
64/9 ÷ 24 = ar⁵ / ar²
64/9 × 1/24 = r³
8/27 = r³
Take the cube root of both side
r = 3√(8/27)
r = 2/3
Thus, the common ratio is 2/3
Aii. Determination of the first term (a).
T3 = ar²
3rd term (T3) = 24
Common ratio (r) = 2/3
First term (a) =?
24 = a(2/3)²
24 = 4a/9
Cross multiply
24 × 9 = 4a
216 = 4a
Divide both side by 4
a = 216/4
a = 54
Thus, the first term (a) is 54
B. Determination of the sum of the first five terms.
Common ratio (r) = 2/3
First term (a) = 54
Number of term (n) = 5
Sum of first five terms (S5) =?
Sn = a[1 –rⁿ] / 1 – r
S5 = 54[1 – (⅔)⁵] / 1 – ⅔
S5 = 54 [1 – 32/243] / ⅓
S5 = 54 (211/243) × 3
S5 = 54 × 211/81
S5 = 6 × 211/9
S5 = 2 × 211/3
S5 = 422/3
Thus, the sum of the first five terms is 422/3
Answer:
A. 45
Step-by-step explanation:
multiply 15 x 3 =45
Answer:
- housing, $1056
- food, $552
- transportation, $408
- savings, $240
- clothing, $144
Step-by-step explanation:
Multiply the budget total by the percentage for each category:
- housing: 44% × $2400 = $1056
- food: 23% × $2400 = $552
- clothing: 6% × $2400 = $144
- transportation: 17% × $2400 = $408
- savings: 10% × $2400 = $240
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Find "the rest" by subtracting the total of percentages from 100%, or by subtracting the total of budget categories from $2400. Here, everything (not including savings) adds to 90% × $2400 = $2160, so the amount to savings is 10%, or $240.
Answer:
3
Step-by-step explanation:
I believe it is 3 because you are multiplying each number by 3 to get your bigger shape
