Question
Find the 10 th term of the geometric sequence
Answer Attempt 1 out of 3
Watch Video
Submit Answer

Question

Question Find the 10 th term of the geometric sequence $$ 9,-18,36, \ldots $$ Answer Attempt 1 out of 3 Watch Video Submit Answer

UpStudy AI · Accepted Answer

1. The first term is $$a = 9$$ and the common ratio is found by
   $$
   r = \frac{-18}{9} = -2.
   $$

2. The general term of a geometric sequence is given by
   $$
   a_n = a \cdot r^{n-1}.
   $$

3. For the 10th term,
   $$
   a_{10} = 9 \cdot (-2)^{10-1} = 9 \cdot (-2)^9.
   $$

4. Calculate $$(-2)^9$$:
   $$
   (-2)^9 = -512.
   $$

5. Multiplying by the first term:
   $$
   a_{10} = 9 \cdot (-512) = -4608.
   $$

The 10th term of the sequence is $$-4608$$.
The 10th term of the sequence is $$-4608$$.

Upstudy AI Solution