The value of y varies directly with x. If x=3, then y=21. What is the value of x when y=105?
1 answer:
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Answer:
The sum of the first 9 terms in the geometric series is 127.75
Step-by-step explanation:
In the geometric series, there is a constant ratio between each two consecutive numbers
<u>Examples:</u>
5, 10, 20, 40, 80, ………………………. (×2)
5000, 1000, 200, 40, …………………………(÷5)
General term (nth term) of a Geometric series is
<em>a1</em> = <em>a</em>, <em>a2</em> = <em>ar</em>, <em>a3</em> = <em>ar</em>², <em>a4</em> = <em>ar</em>³, ..........
, where
<em>a </em>is the first term
r is the constant ratio between each two consecutive terms
The sum of the first <em>n</em> terms of a Geometric series is calculated by this rule
Let us solve the question
∵ The geometric series is 64, 32, 16, .......................
∴ <em>a </em>= 64
∴ <em>r </em>= 32 ÷ 64 = 0.5
→ We need to find the sum of the first 9 terms
∴ <em>n</em> = 9
→ Substitute these values on the formula of the sum above
∴
→ use the calculator to find the answer
∴ <em>S</em>9 = 127.75
∴ The sum of the first 9 terms in the geometric series is 127.75