This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the first term, last term, and common difference. The natural numbers must be between 250 and 550, and divisible by 5. The first number greater than 250 that is divisible by 5 is 255. So, the first term a = 255. The last number less than 550 that is divisible by 5 is 545. So, the last term l = 545. Since the numbers are divisible by 5, the common difference d = 5. Step 2: Calculate the number of terms (n). We use the formula for the n-th term of an arithmetic progression: l = a + (n-1)d. 545 = 255 + (n-1)5 Subtract 255 from both sides: 545 - 255 = (n-1)5 290 = (n-1)5 Divide by 5: (290)/(5) = n-1 58 = n-1 Add 1 to both sides: n = 58 + 1 n = 59 There are 59 numbers in the sequence. Step 3: Calculate the sum of the arithmetic progression. We use the formula for the sum of an arithmetic progression: S_n = (n)/(2)(a + l). S_59 = (59)/(2)(255 + 545) S_59 = (59)/(2)(800) S_59 = 59 × 400 S_59 = 23600 The sum of all natural numbers between 250 and 550 which are divisible by 5 is 23600. That's 2 down. 3 left today — send the next one.