In a mobile data plan, 5 GB of data is given on the first day and 3 GB more each next day. How much data is given on the 16th day?
Answer and explanation
Correct answer: 50 GB
The daily data amounts form an arithmetic progression because the amount increases by the same quantity, 3 GB, each day. Here the first term is a = 5 and the common difference is d = 3. To find the amount on the 16th day, use the nth-term formula a_n = a + (n - 1)d. Substituting the values gives a_16 = 5 + (16 - 1) × 3 = 5 + 15 × 3 = 5 + 45 = 50 GB. Hence option B is correct. Option A results from using only 14 increases, while option C adds one extra 3-GB increase; option D reflects two extra increases. The key is that the first day is the first term, so only 15 increases occur before day 16.
Frequently asked questions
What is the correct answer to this question?
50 GB
Why is this the correct answer?
The daily data amounts form an arithmetic progression because the amount increases by the same quantity, 3 GB, each day. Here the first term is a = 5 and the common difference is d = 3. To find the amount on the 16th day, use the nth-term formula a_n = a + (n - 1)d. Substituting the values gives a_16 = 5 + (16 - 1) × 3 = 5 + 15 × 3 = 5 + 45 = 50 GB. Hence option B is correct. Option A results from using only 14 increases, while option C adds one extra 3-GB increase; option D reflects two extra increases. The key is that the first day is the first term, so only 15 increases occur before day 16.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Word problems based on APs.
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