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4 votes
Write an explicit formula for an, the nth term of the sequence 39,31,23

2 Answers

6 votes

Answer:


a_n=47-8n

Explanation:

Given sequence:

  • 39, 31, 23, ...

Calculate the differences between the terms:


39 \underset{-8}{\longrightarrow} 31 \underset{-8}{\longrightarrow} 23

As the differences are constant (the same), this is an arithmetic sequence with:

  • First term (a) = 39
  • Common difference (d) = -8


\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\end{minipage}}

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:


\implies a_n=39+(n-1)(-8)


\implies a_n=39-8n+8


\implies a_n=47-8n

User Max Lybbert
by
6.4k points
2 votes

Answer:

a_n = 47 - 8n

Explanation:

a_1 = 39

a_2 = 31

a_3 = 23

31 - 39 = -8

23 - 31 = -8

This is an arithmetic sequence with constant difference -8.

a_1 = 39

a_2 = 39 - 8

a_3 = 39 - 8 - 8 = 39 - 2(8)

a_4 = 39 - 8 - 8 - 8 = 39 - 3(8)

...

a_n = 39 - (n - 1)(8)

a_n = 39 - 8(n - 1)

a_n = 39 - 8n + 8

a_n = 47 - 8n

User Erdemus
by
7.1k points
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