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Mathematics
Layne Schaefer
21 December, 08:58
If aₙ = 3 (3) ⁿ⁻1, what is S₃?
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Aaden Lin
21 December, 11:11
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S3 = 39
Step-by-step explanation:
* an = 3 (3) ^ (n-1) is a geometric sequence
* The general rule of the geometric sequence is:
an = a (r) ^ (n-1)
Where:
a is the first term
r is the common difference between each consecutive terms
n is the position of the term in the sequence
The rules means:
- a1 = a, a2 = ar, a3 = ar², a4 = ar³, ...
∵ an = 3 (3) ^ (n-1)
∴ a = 3 and r = 3
∴ a1 = 3
∴ a2 = 3 (3) = 9
∴ a3 = 3 (3) ² = 27
* S3 = a1 + a2 + a3
∴ S3 = 3 + 9 + 27 = 39
Note:
We can use the rule of the sum:
Sn = a (1 - r^n) / (1 - r)
S3 = 3 (1 - 3³) / 1 - 3 = 3 (1 - 27) / -2 = 3 (-26) / -2 = 3 (13) = 39
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Captain
21 December, 11:43
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The correct answer is S₃ = 39
Step-by-step explanation:
It is given that,
aₙ = 3 (3) ⁿ⁻¹
To find a₁
a₁ = 3 (3) ¹⁻¹ = 3 (3) °
= 3 * 1 = 3
To find a₂
a₂ = 3 (3) ²⁻¹ = 3 (3) ¹
= 3 * 3 = 9
To find a₃
a₃ = 3 (3) ³⁻¹ = 3 (3) ²
= 3 * 9 = 27
To find the value of S₃
S₃ = a₁ + a₂ + a₃
= 3 + 9 + 27 = 39
Therefore the correct answer is S₃ = 39
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