Question

If aₙ = 3(3)ⁿ⁻1 , what is S₃?

Answer 1

S3 = 39

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

Answer 2

The correct answer is S₃ = 39

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