The first term of a geometric sequence is 7, and the 7th term is 5103. What is the 5th term?
To solve this problem, I need to recall the formula for the nth term of a geometric sequence: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and a_n is the nth term. I can use this formula to find the common ratio r, since I know a_1 and a_7. Plugging in the values, I get 5103 = 7 * r^(7-1). Dividing both sides by 7, I get 729 = r^6. Taking the sixth root of both sides, I get r = 3. Now that I have the common ratio, I can use the formula again to find the 5th term, a_5. Plugging in the values, I get a_5 = 7 * 3^(5-1). Simplifying, I get a_5 = 7 * 81. Multiplying, I get a_5 = 567. 