Write an
explicit formula for An, the nth term of the sequence 7, -42, 252, ....

Answer:

[tex]A_n = 7(-6)^{n-1}[/tex]

Step-by-step explanation:

Key skills needed: Explicit formula, Geometric sequence

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7   or   252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

[tex]a_n = a_1(r)^{n-1}[/tex]

--> r means the constant (or common ratio) that is being multiplied.

--> [tex]a_1[/tex] means the first term

--> [tex]a_n[/tex] means the "nth" numbered term (so [tex]a_3[/tex] is the 3rd term, [tex]a_{10}[/tex] is the 10th term and so on).

--> [tex]n-1[/tex] is just the "n" in [tex]a_n[/tex] minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> [tex]r = -6[/tex] (Since we got -6 as the constant/common ratio).

--> [tex]a_1 = 7[/tex] (Since 7 is the 1st term)

This means that our formula would be --> [tex]A_n = 7(-6)^{n-1}[/tex]

Hope you understood and have a nice day!! :D

EASY QUESTION!! is 12.0095 the same as 12.95?

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