Question

Ravi is putting up a fence in his backyard. He builds 3 units the first day, 7 units the second day, and 11 units the third day. If he continues this pattern, how many days will it take him to finish the 55 unit fence?

Answer 1

Ravi builds the fence in an arithmetic sequence, adding 4 units to the previous day's work. By summing the units he builds each day, we find that it will take him 5 days to complete the 55 unit fence.

Step-by-step explanation:

Ravi is working on a pattern where he builds more units of his fence each day by increasing the number of units by 4. He builds 3 units on the first day, 7 on the second, 11 on the third, and so on. This is an arithmetic sequence, and to find out how many days it will take him to finish the 55 unit fence, we sum the number of units he builds each day until we reach or exceed 55 units.

Let's write down the sequence to see the pattern more clearly:

• Day 1: 3 units
• Day 2: 7 units
• Day 3: 11 units
• Day 4: 15 units (we add 4 each day)

Now, we continue this sequence and keep a running total:

1. Day 1: 3 units
2. Day 2: 3 + 7 = 10 units total
3. Day 3: 10 + 11 = 21 units total
4. Day 4: 21 + 15 = 36 units total
5. Day 5: 36 + 19 = 55 units total

So, it will take Ravi 5 days to finish the 55 unit fence.