in a geometric sequence the second term is 15 and the 4th term is 135, what is the first term?
Answer (1)
Answer:Here's how to solve this problem: Understanding Geometric Sequences A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant value called the common ratio (often denoted as 'r'). Setting up Equations Let's denote the first term as 'a'. We know the following:Second term (a₂): 15 = a * rFourth term (a₄): 135 = a * r³ Solving for the Common Ratio (r) We can solve for 'r' by dividing the equation for the fourth term by the equation for the second term:135/15 = (a * r³)/(a * r) This simplifies to:9 = r² Taking the square root of both sides, we get:r = ±3 (The common ratio could be either 3 or -3) Solving for the First Term (a) Now we can substitute the value of 'r' back into the equation for the second term to solve for 'a':If r = 3: 15 = a * 3 => a = 15/3 = 5If r = -3: 15 = a * (-3) => a = 15/(-3) = -5 Therefore, the first term (a) could be either 5 or -5. There are two possible geometric sequences that fit the given information.
