Q 18. The fifth term of an arithmetic sequence is 11 , and the tenth term is 41 . What is the FIRST term? \( a_{1}=6 \) \( a_{1}=9 \) \( a_{1}=-13 \) \( a_{1}=-19 \)

To solve for the first term of the arithmetic sequence, we can use the formula for the nth term: \( a_n = a_1 + (n-1)d \), where \( d \) is the common difference and \( a_1 \) is the first term. We know that: 1. For the fifth term: \( a_5 = a_1 + 4d = 11 \) 2. For the tenth term: \( a_{10} = a_1 + 9d = 41 \) From these two equations, we can set up a system to find \( a_1 \) and \( d \). Subtracting the first equation from the second gives us \( 5d = 30 \), so \( d = 6 \). Plugging \( d = 6 \) back into the first equation, we find \( a_1 = 11 - 4 \times 6 = -13 \). Therefore, the first term \( a_1 = -13 \) is the correct choice! The world of arithmetic sequences isn’t just for math enthusiasts! These patterns can be found in everyday scenarios, like saving money, where you add a fixed amount every month, or even scoring points in a game! Finding the first term is like uncovering the ‘hidden treasure’ of your sequence, revealing how it all started! For those way into numbers, a deeper dive into sequences can spark excitement. You might explore series convergence, Fibonacci sequences, or even quadratic sequences! Books on these topics can often offer fascinating insights and some surprisingly quirky applications. Get ready to see numeric patterns pop up everywhere, like your new best friends in math!