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HELP The recursive rule for a sequence is shown An=An-1 +4 a1=14 write the explicit rule in simplified form for the sequence An=

Answer :

MHANIFAGO

Answer:

  • aₙ = 4n + 10

Step-by-step explanation:

Given is the AP with

  • The first term of 14
  • The common difference of 4

Explicit rule for the sequence is

  • [tex]a_n=a_1+(n-1)d=14+(n-1)(4)=14+4n-4=4n+10[/tex]
SEMSEE45GO

Answer:

[tex]\sf a_n=4n+10[/tex]

Step-by-step explanation:

A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

Given recursive rule:

[tex]\begin{cases} \sf a_n=a_{n-1}+4\\ \sf a_1=14\end{cases}[/tex]

Therefore, the next two values in the sequence are:

[tex]\begin{aligned} \implies \sf a_2 & = \sf a_{2-1}+4\\& = \sf a_1+4\\& = \sf 14+4\\& = \sf 18\end{aligned}[/tex]

[tex]\begin{aligned} \implies \sf a_3 & =\sf a_{3-1}+4\\& = \sf a_2+4\\& = \sf 18+4\\& = \sf 22\end{aligned}[/tex]

Explicit formula

  [tex]\sf a_n=a+(n-1)d[/tex]

where:

  • [tex]\sf a_n[/tex] is the nth term
  • a is the first term
  • n is the number of the term
  • d is the common difference between terms

Given:

  • [tex]\sf a = a_1=14[/tex]
  • [tex]\sf d = 22-18=4[/tex]

Substituting the given values into the formula:

[tex]\sf \implies a_n=14+(n-1)4[/tex]

[tex]\sf \implies a_n=14+4n-4[/tex]

[tex]\sf \implies a_n=4n+10[/tex]

Therefore, the explicit rule in simplified form for the sequence is:

[tex]\sf a_n=4n+10[/tex]

Learn more about arithmetic sequences here:

https://brainly.com/question/27806372

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