Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

An expression for the nth term of a geometric sequence is:

[tex]\[ 6 \times 3^{n-1} \][/tex]

Write down the first 3 terms of this sequence.


Sagot :

To determine the first three terms of the geometric sequence given by the expression
[tex]\[ 6 \times 3^{n-1} \][/tex]
we will substitute [tex]\( n \)[/tex] with the values 1, 2, and 3.

1. First Term:

Substitute [tex]\( n = 1 \)[/tex] into the expression:
[tex]\[ 6 \times 3^{1-1} \][/tex]

Since [tex]\( 1-1\)[/tex] equals 0 , we have:
[tex]\[ 6 \times 3^0 \][/tex]

We know that any number raised to the power of 0 is 1:
[tex]\[ 3^0 = 1 \][/tex]

Thus, the first term is:
[tex]\[ 6 \times 1 = 6 \][/tex]

2. Second Term:

Substitute [tex]\( n = 2 \)[/tex] into the expression:
[tex]\[ 6 \times 3^{2-1} \][/tex]

Since [tex]\( 2-1\)[/tex] equals 1 , we have:
[tex]\[ 6 \times 3^1 \][/tex]

We know that any number raised to the power of 1 remains the same:
[tex]\[ 3^1 = 3 \][/tex]

Thus, the second term is:
[tex]\[ 6 \times 3 = 18 \][/tex]

3. Third Term:

Substitute [tex]\( n = 3 \)[/tex] into the expression:
[tex]\[ 6 \times 3^{3-1} \][/tex]

Since [tex]\( 3-1\)[/tex] equals 2 , we have:
[tex]\[ 6 \times 3^2 \][/tex]

We know that [tex]\( 3^2 = 3 \times 3 = 9 \)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]

Thus, the third term is:
[tex]\[ 6 \times 9 = 54 \][/tex]

Therefore, the first three terms of the sequence are:
[tex]\[ 6, 18, 54 \][/tex]