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17 Mar 2026, 22:11
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D
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Difficulty:
65%
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Question Stats:
64% (02:48) correct
36%
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wrong
based on 184
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Desislava made a deposit each day in July into a bank account. The amounts deposited formed an arithmetic sequence. She deposited x-45 dollars on July 6 and x-15 dollars on July 16. How many dollars did Desislava deposit in the last 11 days of the month?
A. 11x + 110
B. 11x + 132
C. 11x + 150
D. 11x + 165
E. 11x + 198
A. 11x + 110
B. 11x + 132
C. 11x + 150
D. 11x + 165
E. 11x + 198
18 Mar 2026, 16:49
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Let's break this down step by step.
Step 1: Find the common difference.
In an arithmetic sequence, deposits increase by the same amount each day. July 6 deposit is (x - 45) and July 16 deposit is (x - 15). That's a difference of 10 days.
Increase over 10 days = (x - 15) - (x - 45) = 30 dollars.
So the daily increase (common difference) = 30 / 10 = 3 dollars per day.
Step 2: Find the deposit on July 1.
July 6 is the 6th term. Working backwards 5 days from July 6:
July 1 deposit = (x - 45) - 5(3) = x - 45 - 15 = x - 60.
Step 3: Write the general formula.
The deposit on day n is: (x - 60) + (n - 1)(3) = x - 63 + 3n.
Step 4: Find the sum for the last 11 days (July 21 to July 31).
July 21 deposit (n = 21): x - 63 + 63 = x
July 31 deposit (n = 31): x - 63 + 93 = x + 30
The sum of an arithmetic sequence = (number of terms / 2) × (first term + last term).
Sum = (11 / 2) × (x + x + 30) = (11 / 2) × (2x + 30) = 11 × (x + 15) = 11x + 165.
Answer: D
Key principle: In arithmetic sequence problems, always find the common difference first, then use the sum formula: Sum = (number of terms / 2) × (first term + last term).
Step 1: Find the common difference.
In an arithmetic sequence, deposits increase by the same amount each day. July 6 deposit is (x - 45) and July 16 deposit is (x - 15). That's a difference of 10 days.
Increase over 10 days = (x - 15) - (x - 45) = 30 dollars.
So the daily increase (common difference) = 30 / 10 = 3 dollars per day.
Step 2: Find the deposit on July 1.
July 6 is the 6th term. Working backwards 5 days from July 6:
July 1 deposit = (x - 45) - 5(3) = x - 45 - 15 = x - 60.
Step 3: Write the general formula.
The deposit on day n is: (x - 60) + (n - 1)(3) = x - 63 + 3n.
Step 4: Find the sum for the last 11 days (July 21 to July 31).
July 21 deposit (n = 21): x - 63 + 63 = x
July 31 deposit (n = 31): x - 63 + 93 = x + 30
The sum of an arithmetic sequence = (number of terms / 2) × (first term + last term).
Sum = (11 / 2) × (x + x + 30) = (11 / 2) × (2x + 30) = 11 × (x + 15) = 11x + 165.
Answer: D
Key principle: In arithmetic sequence problems, always find the common difference first, then use the sum formula: Sum = (number of terms / 2) × (first term + last term).
