To find the first, fourth, and eighth terms of the sequence \( A(n) = -5 \cdot 3^n - 1 \), we will substitute \( n = 1 \), \( n = 4 \), and \( n = 8 \) into the sequence formula.
**First term (\( n = 1 \)):**
\[ A(1) = -5 \cdot 3^1 - 1 \]
\[ A(1) = -5 \cdot 3 - 1 \]
\[ A(1) = -15 - 1 \]
\[ A(1) = -16 \]
**Fourth term (\( n = 4 \)):**
\[ A(4) = -5 \cdot 3^4 - 1 \]
\[ A(4) = -5 \cdot (3 \cdot 3 \cdot 3 \cdot 3) - 1 \]
\[ A(4) = -5 \cdot 81 - 1 \]
\[ A(4) = -405 - 1 \]
\[ A(4) = -406 \]
**Eighth term (\( n = 8 \)):**
\[ A(8) = -5 \cdot 3^8 - 1 \]
\[ A(8) = -5 \cdot (3^8) - 1 \]
To find \( 3^8 \):
\[ 3^2 = 9 \]
\[ 3^4 = 81 \]
\[ 3^8 = 81 \cdot 81 = 6561 \]
So,
\[ A(8) = -5 \cdot 6561 - 1 \]
\[ A(8) = -32805 - 1 \]
\[ A(8) = -32806 \]
Therefore, the first term \( A(1) \) is \(-16\), the fourth term \( A(4) \) is \(-406\), and the eighth term \( A(8) \) is \(-32806\).
Comparing these values to the given options:
- \( \text{Option 1}: 1; -3375; -170859375\)
- \( \text{Option 2}: -45; -1215; -98415\)
- \( \text{Option 3}: -15; -405; -32805\)
- \( \text{Option 4}: -5; -135; -10935\)
None of the options match the calculated terms directly. If there was a typographical error to correct in the problem, it should instead match these terms:
- 1st term: -16
- 4th term: -406
- 8th term: -32806.
Rechecking and trivial options suggest we might reconsider context or error in provided options.
6.
Find the first, fourth, and eighth terms of the sequence.
A(n) = −5 ∙ 3x − 1
1; –3,375; –170,859,375
–45; –1,215; –98,415
–15; –405; –32,805
–5; –135; –10,935
1 answer