At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
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]
[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]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.