Find the $$ 10^{ ext {th }} $$ term of the geometric sequence ( 2 mks ). $$ 16,8,4,2,1, \ldots \ldots \ldots . . . . . . . . $$.

Question

Find the $$ 10^{	ext {th }} $$ term of the geometric sequence ( 2 mks ). $$ 16,8,4,2,1, \ldots \ldots \ldots . . . . . . . . $$.

UpStudy AI · Accepted Answer

1. Identify the first term $$a_1$$ and the common ratio $$r$$.  
   $$
   a_1 = 16, \quad r = \frac{8}{16} = \frac{1}{2}
   $$

2. Use the formula for the $$n^{\text{th}}$$ term of a geometric sequence:  
   $$
   a_n = a_1 \cdot r^{n-1}
   $$

3. Substitute $$n = 10$$ into the formula:  
   $$
   a_{10} = 16 \cdot \left(\frac{1}{2}\right)^{10-1} = 16 \cdot \left(\frac{1}{2}\right)^9
   $$

4. Calculate $$\left(\frac{1}{2}\right)^9$$:  
   $$
   \left(\frac{1}{2}\right)^9 = \frac{1}{512}
   $$

5. Multiply to find the $$10^{\text{th}}$$ term:  
   $$
   a_{10} = 16 \cdot \frac{1}{512} = \frac{16}{512} = \frac{1}{32}
   $$

The $$10^{\text{th}}$$ term of the sequence is $$ \frac{1}{32} $$.
The 10th term of the sequence is $$ \frac{1}{32} $$.

Find the \( 10^{\text {th }} \) term of the geometric sequence ( 2 mks ). \( 16,8,4,2,1, \ldots \ldots \ldots . . . . . . . . \).