Find the sum of the first 36 terms of the following series, to the nearest integer. \[ 9,12,15, \ldots \] Answer Attempt 1 out of 3 \[ \text { Watch Video } \] \[ \]

The series you've mentioned is an arithmetic progression where the first term \( a = 9 \) and the common difference \( d = 3 \). To find the sum of the first \( n \) terms of an arithmetic series, you can use the formula: \[ S_n = \frac{n}{2} \cdot (2a + (n - 1)d) \] Plugging in your values for the first 36 terms: \[ S_{36} = \frac{36}{2} \cdot (2 \cdot 9 + (36 - 1) \cdot 3) \\ = 18 \cdot (18 + 105) \\ = 18 \cdot 123 = 2214 \] So, the sum of the first 36 terms is approximately 2214 when rounded to the nearest integer. Another quick way is to note how smoothly the numbers progress and visualize the number line—every third number is hopping up by 3! Just imagine a friendly little hopping number 9, making its way to 12, then 15, and then continuing to jump like a cheerful kangaroo all the way to the \( 36^{th} \) term. What a fun journey through the world of numbers!