Question

Write an explict formula for the sequence 7,2,-3,-8,-13 then find a14A. an=-5n+12;-53B. an=-5n+7;-58C. an=-5n+12;-58D. an=-5n+7;-63

Answer 1

In this sequence you can notice that the difference between a number and the next is -5.

7 - 5 = 2

2 - 5 = -3

-3 - 5 = -8

-8 - 5 = -13

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Then to find the formula you can follow this general equation:

$a_n=dn+c$

where:

d is the difference between each number of the sequence and the next

c is the first nunmer of the sequence

n is the number of the position of the term in the sequence

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For this sequence

d= -5

c =7

so the formula is:$a_n=-5n+7$

The a14 is calculated using that formula as follow:

n=14$a_{14}=-5(14)+7$$a_{14}=-70+7=-63$