Write a recursive formula for the sequence \( 7,13,19,25,31, \ldots \) Then find the next term. \( \begin{array}{l}\text { a. } a_{n}=a_{n-1}+6 \text {, where } a_{1}=7 ; 37 \\ \text { b. } a_{n}=a_{n-1}+6 \text {, where } a_{1}=37 ; 7 \\ \text { c. } a_{n}=a_{n-1}-6 \text {, where } a_{1}=7 ; 37 \\ \text { d. } a_{n}=a_{n-1}-6 \text {, where } a_{1}=6 ;-23\end{array} \)
Solución de inteligencia artificial de Upstudy
Responder
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Mind Expander
The sequence provided is an arithmetic sequence, where each term increases by 6. This establishes that the recursive formula should indeed be \( a_{n} = a_{n-1} + 6 \), starting from \( a_{1} = 7 \). To find the next term following \( 31 \), we calculate \( 31 + 6 = 37 \). So, the answer is \( a. \) \( a_{n}=a_{n-1}+6 \text{, where } a_{1}=7 ; 37 \). Keep up the math momentum! Understanding recursive formulas in sequences like this can help with more complex problems down the line. It’s the key to unveiling patterns, and guess what? Patterns are everywhere!
