Answer :
Sure! Let's solve this step by step.
We are given an arithmetic sequence where the first few bids are: [tex]\( 196, 208, 220, 232, \ldots \)[/tex]
The explicit formula for the nth term of this sequence is:
[tex]\[ A_n = 12(n-1) + 196 \][/tex]
We need to find the tenth bid, which means we need to find [tex]\( A_{10} \)[/tex].
Step-by-Step Solution:
1. Identify the first term ([tex]\( A_1 \)[/tex]) of the sequence:
[tex]\[ A_1 = 196 \][/tex]
2. Determine the common difference ([tex]\( d \)[/tex]) of the sequence:
[tex]\[ d = 208 - 196 = 12 \][/tex]
3. Plug [tex]\( n = 10 \)[/tex] into the explicit formula:
[tex]\[ A_{10} = 12(10-1) + 196 \][/tex]
4. Simplify inside the parentheses first:
[tex]\[ 10 - 1 = 9 \][/tex]
5. Multiply the common difference by 9:
[tex]\[ 12 \times 9 = 108 \][/tex]
6. Add this result to the first term:
[tex]\[ 108 + 196 = 304 \][/tex]
Therefore, the tenth bid in the sequence is:
[tex]\[ A_{10} = 304 \][/tex]
So, the tenth bid is $304.
We are given an arithmetic sequence where the first few bids are: [tex]\( 196, 208, 220, 232, \ldots \)[/tex]
The explicit formula for the nth term of this sequence is:
[tex]\[ A_n = 12(n-1) + 196 \][/tex]
We need to find the tenth bid, which means we need to find [tex]\( A_{10} \)[/tex].
Step-by-Step Solution:
1. Identify the first term ([tex]\( A_1 \)[/tex]) of the sequence:
[tex]\[ A_1 = 196 \][/tex]
2. Determine the common difference ([tex]\( d \)[/tex]) of the sequence:
[tex]\[ d = 208 - 196 = 12 \][/tex]
3. Plug [tex]\( n = 10 \)[/tex] into the explicit formula:
[tex]\[ A_{10} = 12(10-1) + 196 \][/tex]
4. Simplify inside the parentheses first:
[tex]\[ 10 - 1 = 9 \][/tex]
5. Multiply the common difference by 9:
[tex]\[ 12 \times 9 = 108 \][/tex]
6. Add this result to the first term:
[tex]\[ 108 + 196 = 304 \][/tex]
Therefore, the tenth bid in the sequence is:
[tex]\[ A_{10} = 304 \][/tex]
So, the tenth bid is $304.
