Pregunta
3.4 Is -72 a term in the sequence? Justify your answer.
Which term in the sequence
has a value of 8 ?
Which term in the sequence
Ask by Goodwin Watson. in South Africa
Dec 16,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The 31st term of the sequence is 8. -72 is not a term in the sequence.
Solución
To determine if -72 is a term in the given sequence, we first need to identify the pattern of the sequence. Let’s look at the differences between consecutive terms:
It appears that the difference between consecutive terms is consistently
. This suggests that the sequence is an arithmetic sequence with a common difference of
.
To find the term that equals 8, we can use the formula for the nth term of an arithmetic sequence:
where
is the nth term,
is the first term,
is the term number, and
is the common difference.
In this case,
and
. We want to find the value of
such that
:
Let’s solve for
:
So, the 31st term of the sequence is 8.
Now, let’s check if -72 is a term in the sequence. We can use the same formula to find the term number for -72:
Solving for
:
Since
is a negative number, it is not possible for the sequence to have a negative term number. Therefore, -72 is not a term in the given sequence.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg


Mind Expander
To determine if -72 is a term in the sequence given as
, we need to analyze the pattern. The sequence appears to be an arithmetic sequence where each term is generated by adding a common difference. The common difference can be calculated as
. Continuing this sequence, we can see that all terms remain negative, so -72 is not a term in the sequence.
To find which term in the sequence equals 8, we can set the nth term formula for an arithmetic sequence:
. Here,
and
. Setting
, we can solve for
:
Simplifying this gives:
So, the 31st term in the sequence has a value of 8!
preguntas relacionadas

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium