Find the sum of the first 15 multiples of 8.
Understand the Problem
The question is asking to find the sum of the first 15 multiples of 8, which involves a basic arithmetic calculation.
Answer
The sum of the first 15 multiples of 8 is $960$.
Answer for screen readers
The sum of the first 15 multiples of 8 is $960$.
Steps to Solve
- Identify the first 15 multiples of 8 To find the first 15 multiples of 8, multiply 8 by integers from 1 to 15.
The multiples are: $$ 8 \times 1, 8 \times 2, 8 \times 3, \ldots, 8 \times 15 $$
- Calculate the sum of these multiples The sum can be calculated as: $$ S = 8 \times 1 + 8 \times 2 + 8 \times 3 + ... + 8 \times 15 $$
Factoring out the common term (8): $$ S = 8 \times (1 + 2 + 3 + ... + 15) $$
- Use the formula for the sum of the first n natural numbers The formula for the sum of the first n natural numbers is: $$ \text{Sum} = \frac{n(n + 1)}{2} $$
For our case, ( n = 15 ): $$ \text{Sum} = \frac{15(15 + 1)}{2} = \frac{15 \times 16}{2} = 120 $$
- Calculate the final sum Substituting back, we get: $$ S = 8 \times 120 = 960 $$
The sum of the first 15 multiples of 8 is $960$.
More Information
The first 15 multiples of 8 are part of an arithmetic series, and summing them demonstrates how numerical patterns can be utilized to simplify calculations.
Tips
- Forgetting to factor out the common multiple (8) can lead to errors.
- Not using the correct formula for the sum of natural numbers, resulting in incorrect calculations.
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