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Sagot :
Given the sequence:
23, 16, 9, 2
Use the arithmetic sequence formula:
[tex]a_n=a_1+(n-1)d[/tex]Where
an = nth term
a1 = first term
n = number of terms
d = common difference
d = a2 - a1 = 16-23 = -7
Since d = -7, let's find the equation for the nth term.
[tex]\begin{gathered} a_n=23+(n-1)-7 \\ a_n=23+n(-7)-1(-7) \\ a_n=23-7n+7 \\ \text{Combine like terms} \\ a_n=-7n\text{ +23}+7 \\ \\ a_n=-7n+30 \end{gathered}[/tex]The equation for the nth term is:
[tex]a_n=-7n+30[/tex]Let's find the 25th term, a25:
Substitute n for 25 and evaluate
[tex]\begin{gathered} a_{25}=-7(25)+20 \\ \\ a_{25}=-175+30 \\ \\ a_{25}=-145 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} a_n=-7n+30 \\ \\ \\ a_{25}=-145 \end{gathered}[/tex]
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