Find the second, fourth, and tenth terms of the sequence described by the rule.
A(n) = 13 + (n - 1)(12)
A(2) = [ ] (Type an integer or a decimal.)
To find the second term of the sequence, we substitute n = 2 into the rule and calculate A(2):
A(2) = 13 + (2 - 1)(12)
A(2) = 13 + (1)(12)
A(2) = 13 + 12
A(2) = 25
So, the second term of the sequence is 25.
A(4) = [ ] (type an integer or decimal)
To find the fourth term of the sequence, we substitute n = 4 into the rule and calculate A(4):
A(4) = 13 + (4 - 1)(12)
A(4) = 13 + (3)(12)
A(4) = 13 + 36
A(4) = 49
So, the fourth term of the sequence is 49.
A(10) = [ ] (type an integer or decimal)
To find the tenth term of the sequence, we substitute n = 10 into the rule and calculate A(10):
A(10) = 13 + (10 - 1)(12)
A(10) = 13 + (9)(12)
A(10) = 13 + 108
A(10) = 121
So, the tenth term of the sequence is 121.
You borrow $525 from a friend the first week and pay the friend back $20 each week thereafter. Write the first six terms in the sequence. Explain what the sixth term means in the context of the situation.
Write the first six terms in the sequence.
The first term is
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The second term is
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The third term is
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The fourth term is
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The fifth term is
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The sixth term is
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The sequence described in the given situation is an arithmetic sequence where the first term is $525 and each subsequent term is obtained by subtracting $20 from the previous term.
The first term is $525.
The second term is $525 - $20 = $505.
The third term is $505 - $20 = $485.
The fourth term is $485 - $20 = $465.
The fifth term is $465 - $20 = $445.
The sixth term is $445 - $20 = $425.
Explanation of the sixth term in the context of the situation: The sixth term, $425, represents the amount of money owed to the friend after 6 weeks of borrowing and repaying $20 each week. It shows that the borrower has repaid a total of $20 x (6 - 1) = $100 and still owes $425 to the friend.