Respuesta :
Answer:
843
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 24 and d = - 7 - (- 24) = - 7 + 24 = 17, thus
[tex]a_{52}[/tex] = - 24 + (51 × 17) = - 24 + 867 = 843
The 52nd term of the arithmetic sequence is 843.
How to find the 52nd term of the arithmetic sequence?
The terms, -24,-7, and 10 exist in AP and continued in the same sequence.
Here, a = first term
N = number of terms
d = common difference
[tex]$a_{n}=$[/tex] last term
Common difference = -7 - (-24) = 17
Hence, common difference = 17
Number of terms = 52
First-term = -24
we know that,
[tex]$a_{n}=a+(n-1) d$[/tex]
According to this formula,
[tex]${data-answer}amp;a_{n}=-24+(52-1) 17 \\[/tex]
[tex]${data-answer}amp;\Longrightarrow a_{n}=-24+(51) 17 \\[/tex]
[tex]${data-answer}amp;\Longrightarrow a_{n}=-24+867 \\[/tex]
[tex]$a_{n}=843[/tex]
Therefore, the 52nd term of the arithmetic sequence is 843.
To learn more about arithmetic sequence
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