Question

The 5th term of a geometric Sequence is 8 and the 9th term Is 16128.find the first term

Answer 1

$First \ term \ GP = a\\ Second\ term = ar\\ Third \ term = ar\\^2\\ 5th\ term = ar\\^4\\ 9th\ term = ar\\^8\\ ar\\^4 = 8\\ ar\\^8 = 16128 \\ a = \frac{16128}{r\\^8}\\ \frac{16128}{r\\^8} \times r\\^4 = 8$

$\frac{16128}{r\\^4} = 8 \\ \\ 8r\\^4 = 16128 \\ \frac{16128}{8} = r\\^4 \\ 2016 = r\\^4 \\ r = 6.70 \\a = \frac{8}{r\\^4} \\ a = \frac{8}{(6.7)\\^4} \\ a = 0.00397$