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Given that √ 6, 3√2, 3√6, 9√2 ...... are the first four terms of an exponential sequence G. P , find in its simplest form the 8th term ?
Anonymous
Mar 21
Given that √ 6, 3√2, 3√6, 9√2 ...... are the first four terms of an exponential sequence G. P , find in its simplest form the 8th term ?
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ChatGPT
Mar 21
To find the 8th term of the exponential sequence, we first need to determine the common ratio of the sequence.
From the given terms:
√6, 3√2, 3√6, 9√2
We can see that each term is obtained by multiplying the previous term by √2. Therefore, the common ratio (r) of the sequence is √2.
To find the 8th term, we can use the formula for the nth term of a geometric sequence:
Tn = ar^(n-1)
where:
Tn = the nth term
a = the first term
r = the common ratio
n = the term number
Plugging in the values:
a = √6
r = √2
n = 8
T8 = √6 * (√2)^(8-1)
T8 = √6 * (√2)^7
T8 = √6 * 2^(7/2)
T8 = √6 * 2^3.5
T8 = √6 * 11.3137
T8 = 18
Therefore, the 8th term of the exponential sequence is 18.
From the given terms:
√6, 3√2, 3√6, 9√2
We can see that each term is obtained by multiplying the previous term by √2. Therefore, the common ratio (r) of the sequence is √2.
To find the 8th term, we can use the formula for the nth term of a geometric sequence:
Tn = ar^(n-1)
where:
Tn = the nth term
a = the first term
r = the common ratio
n = the term number
Plugging in the values:
a = √6
r = √2
n = 8
T8 = √6 * (√2)^(8-1)
T8 = √6 * (√2)^7
T8 = √6 * 2^(7/2)
T8 = √6 * 2^3.5
T8 = √6 * 11.3137
T8 = 18
Therefore, the 8th term of the exponential sequence is 18.
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