Question

If aₙ = 3(3)ⁿ⁻¹ , what is S₃? 12 27 9 39

Answer 1

Answer:

$S_3=39$

Step-by-step explanation:

The nth term of the sequence is

$a_n=3(3)^{n-1}$

To get the first term, substitute n=1,

$a_1=3(3)^{1-1}=3$

To get the second term, substitute n=2,

$a_2=3(3)^{2-1}=9$

To get the third term, substitute n=3,

$a_3=3(3)^{3-1}=27$

The sum of the first three terms is

$S_3=3+9+27=39$

We could also use the formula

$S_n=\frac{a_1(r^n-1)}{r-1}$ to get the same result.

Answer 2

Answer:

The correct answer is last option   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 last option   39