4.) If3 geometric means arefind the third geometric meaninserted 6 and 1536,2MO
Answer (1)
Answer:To find the third geometric mean between 6 and 1536, follow these steps:Step 1: Let the three geometric means between 6 and 1536 be G1, G2, and G3. This forms a geometric sequence: 6, G1, G2, G3, 1536.Step 2: Use the formula for the n-th term of a geometric sequence:a_n = a_1 * r^(n-1),where a_n is the n-th term, a_1 is the first term, r is the common ratio, and n is the position of the term.Here, a_1 = 6, a_5 = 1536, and n = 5 (since we are looking for the terms between the first and fifth terms). So,1536 = 6 * r^4.Step 3: Solve for r:1536 / 6 = r^4,256 = r^4,r = 4.Step 4: Now that we know the common ratio is 4, find the third geometric mean (G3) by multiplying the previous term (G2) by the common ratio:G1 = 6 * 4 = 24,G2 = 24 * 4 = 96,G3 = 96 * 4 = 384.Therefore, the third geometric mean is 384.
