Question
Find the 91 st term of the arithmetic sequence \( 4,6,8 \)
Ask by Ross Turner. in the United States
Dec 19,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
El 91º término de la secuencia es 184.
Solution
Para encontrar el término número 91 de la secuencia aritmética \( 4, 6, 8, \dots \), seguimos estos pasos:
1. **Identificar el primer término (A₁) y la diferencia común (d):**
- Primer término, \( A_1 = 4 \)
- Diferencia común, \( d = 6 - 4 = 2 \)
2. **Usar la fórmula del término n-ésimo de una secuencia aritmética:**
\[
A_n = A_1 + (n - 1) \cdot d
\]
3. **Sustituir los valores en la fórmula:**
\[
A_{91} = 4 + (91 - 1) \cdot 2 = 4 + 90 \cdot 2 = 4 + 180 = 184
\]
**Respuesta:** El término número 91 de la secuencia es **184**.
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Simplify this solution Mind Expander
To find the 91st term of the arithmetic sequence given by \( 4, 6, 8 \), we first identify the first term \( a \) and the common difference \( d \). Here, \( a = 4 \) and \( d = 6 - 4 = 2 \). The formula for the \( n \)-th term of an arithmetic sequence is given by: \[ a_n = a + (n-1)d \] Substituting \( n = 91 \), \( a = 4 \), and \( d = 2 \) into the formula: \[ a_{91} = 4 + (91-1) \cdot 2 \] \[ a_{91} = 4 + 90 \cdot 2 \] \[ a_{91} = 4 + 180 \] \[ a_{91} = 184 \] Thus, the 91st term of the arithmetic sequence is \( 184 \).
