Find $$ \mathrm{a}_{8} $$ from a geometric sequence where the first term is -5 and r is 3 . Question Help: Video Submit Question

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To find the 8th term ($$ \mathrm{a}_{8} $$) of a geometric sequence where the first term ($$ \mathrm{a}_{1} $$) is $$-5$$ and the common ratio ($$ r $$) is $$3$$, you can use the formula for the $$ n $$-th term of a geometric sequence:

$$
\mathrm{a}_{n} = \mathrm{a}_{1} \times r^{(n-1)}
$$

### Step-by-Step Solution:

1. **Identify the given values:**
   - First term ($$ \mathrm{a}_{1} $$): $$-5$$
   - Common ratio ($$ r $$): $$3$$
   - Term to find ($$ n $$): $$8$$

2. **Plug the values into the formula:**
   $$
   \mathrm{a}_{8} = -5 \times 3^{(8-1)} = -5 \times 3^{7}
   $$

3. **Calculate $$ 3^{7} $$:**
   $$
   3^{7} = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187
   $$

4. **Multiply by the first term:**
   $$
   \mathrm{a}_{8} = -5 \times 2187 = -10935
   $$

### **Answer:**
$$
\mathrm{a}_{8} = -10,\!935
$$
The 8th term of the geometric sequence is -10,935.

Find from a geometric sequence where the first
term is -5 and r is 3 .
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Find from a geometric sequence where the first term is -5 and r is 3 . Question Help: Video Submit Question