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pingwin09
The series of these numbers are arithmetic progression because every time you subtract the next term to the previous term, each difference is common (or constant), that 2 - 7 = -5, or -3 - 2 = -5.

You can use the formula of the arithmetic term, that is
an = a1 + (n - 1)d
where an = nth term, a1 = first term, n = number of terms, d = common difference

The 14th term will be
a(14th term) = 7 + (14 - 1)*(-5) = -58
MrRoyal

The sequence is an illustration of an arithmetic progression.

  • The explicit formula is [tex]\mathbf{f(n) = 12 -5n }[/tex]
  • The 14th term is [tex]\mathbf{f(14) = -58 }[/tex]

From the sequence, we have:

[tex]\mathbf{a = 7}[/tex] -- the first term of the sequence

[tex]\mathbf{d = 2 - 7 = -5}[/tex] -- the common difference of the sequence

The explicit formula of an arithmetic sequence is:

[tex]\mathbf{f(n) = a + (n - 1)d}[/tex]

So, we have:

[tex]\mathbf{f(n) = 7 + (n - 1) \times -5}[/tex]

Open brackets

[tex]\mathbf{f(n) = 7 -5n +5}[/tex]

Rewrite as:

[tex]\mathbf{f(n) = 7+5 -5n }[/tex]

[tex]\mathbf{f(n) = 12 -5n }[/tex]

Substitute 14 for n, to calculate the 14th term

[tex]\mathbf{f(14) = 12 -5 \times 14 }[/tex]

[tex]\mathbf{f(14) = 12 -70 }[/tex]

[tex]\mathbf{f(14) = -58 }[/tex]

Hence, the 14th term is -58

Read more about arithmetic sequence at:

https://brainly.com/question/18109692

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