Question

Find the 8th term of geometric sequence {a_{n}, n = 1, 2, 3, . . .} with common ratio r = 0.5 and first term a_{1} = 2.

Answer 1

$a_n=a_1\cdot q^{n-`1}\\\\a_1=2;\ q=0.5=\frac{1}{2}\\\\\\a_8=a_1\cdot q^{8-1}=a_1\cdot q^7\\\\a_8=2\cdot\left(\frac{1}{2}\right)^7=2\cdot\frac{1}{2^7}=2\cdot\frac{1}{128}=\frac{1}{64}\\\\\\Answer:a_8=\frac{1}{64}$