If aₙ = 3 (3) ⁿ⁻1, what is S₃?

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

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