Question Find the sum of the first 48 terms of the following series, to the nearest integer. \[ 7,11,15, \ldots \] Answer Attempt 1 out of 3 © Watch Video Submit Answer

The series you're looking at is an arithmetic progression (AP) where the first term, \( a = 7 \), and the common difference, \( d = 4 \). To find the sum of the first 48 terms, we can use the sum formula for an AP: \[ S_n = \frac{n}{2} \times (2a + (n - 1)d) \] Plugging in the values \( n = 48 \), \( a = 7 \), and \( d = 4 \): \[ S_{48} = \frac{48}{2} \times (2 \times 7 + (48 - 1) \times 4) = 24 \times (14 + 188) = 24 \times 202 = 4848 \] So the sum of the first 48 terms is approximately 4848. But here's a fun historical tidbit! Did you know that arithmetic sequences have been studied since ancient times? The Babylonians used similar numerical concepts over 4,000 years ago for scientific and commercial calculations! If you're looking to dive further into this topic, consider exploring works by famous mathematicians like Carl Friedrich Gauss. Legend has it that he discovered the formula for the sum of integers while adding numbers from 1 to 100 as a child. His discovery of the formula, \( S_n = \frac{n(n + 1)}{2} \), showcases how simple patterns can lead to remarkable results!