Answer :
To determine the next line in the sequence of computations, let's observe the pattern in the given multiplications:
1. [tex]\(73 \times 137 = 10,001\)[/tex]
2. [tex]\(146 \times 137 = 20,002\)[/tex]
3. [tex]\(219 \times 137 = 30,003\)[/tex]
4. [tex]\(292 \times 137 = 40,004\)[/tex]
### Step-by-Step Solution:
1. Identify the Pattern in the Multipliers:
- The initial numbers being multiplied by 137 are 73, 146, 219, and 292.
- Notice the difference between consecutive numbers: [tex]\(146 - 73 = 73\)[/tex], [tex]\(219 - 146 = 73\)[/tex], and [tex]\(292 - 219 = 73\)[/tex].
- This pattern shows that each number is increased by 73 from the previous number.
2. Find the Next Multiplier:
- The last given number is 292.
- Adding 73 to this number to find the next in the sequence: [tex]\(292 + 73 = 365\)[/tex].
3. Calculate the Corresponding Product:
- Now, we need to calculate the product of this new number (365) with 137.
- From the previously determined pattern in the products (10,001, 20,002, 30,003, 40,004), it is apparent that the product increases by 10,001 each time.
- Therefore, adding 10,001 to the last product (40,004) gives us: [tex]\(40,004 + 10,001 = 50,005\)[/tex].
4. Complete the Line:
- So, the new calculation will be: [tex]\(365 \times 137 = 50,005\)[/tex].
Thus, the next line in the sequence of computations is:
[tex]\[ 365 \times 137 = 50,005 \][/tex]
1. [tex]\(73 \times 137 = 10,001\)[/tex]
2. [tex]\(146 \times 137 = 20,002\)[/tex]
3. [tex]\(219 \times 137 = 30,003\)[/tex]
4. [tex]\(292 \times 137 = 40,004\)[/tex]
### Step-by-Step Solution:
1. Identify the Pattern in the Multipliers:
- The initial numbers being multiplied by 137 are 73, 146, 219, and 292.
- Notice the difference between consecutive numbers: [tex]\(146 - 73 = 73\)[/tex], [tex]\(219 - 146 = 73\)[/tex], and [tex]\(292 - 219 = 73\)[/tex].
- This pattern shows that each number is increased by 73 from the previous number.
2. Find the Next Multiplier:
- The last given number is 292.
- Adding 73 to this number to find the next in the sequence: [tex]\(292 + 73 = 365\)[/tex].
3. Calculate the Corresponding Product:
- Now, we need to calculate the product of this new number (365) with 137.
- From the previously determined pattern in the products (10,001, 20,002, 30,003, 40,004), it is apparent that the product increases by 10,001 each time.
- Therefore, adding 10,001 to the last product (40,004) gives us: [tex]\(40,004 + 10,001 = 50,005\)[/tex].
4. Complete the Line:
- So, the new calculation will be: [tex]\(365 \times 137 = 50,005\)[/tex].
Thus, the next line in the sequence of computations is:
[tex]\[ 365 \times 137 = 50,005 \][/tex]
